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Tytuł:
Nearly irreducibility of polynomials and the Newton diagrams
Autorzy:
Masternak, Mateusz
Powiązania:
https://bibliotekanauki.pl/articles/1793463.pdf
Data publikacji:
2020-01-22
Wydawca:
Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
Tematy:
irreducibility of polynomials
Newton diagram
Newton polygon
plane algebraic curve
Opis:
Let f be a polynomial in two complex variables. We say that f is nearly irreducible if any two nonconstant polynomial factors of f have a common zero in $C^{2}$. In the paper we give a criterion of nearly irreducibility for a given polynomial f in terms of its Newton diagram.
Źródło:
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica; 2020, 19; 65-77
2300-133X
Pojawia się w:
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A conjugate gradient method with quasi-Newton approximation
Autorzy:
Koko, Jonas
Powiązania:
https://bibliotekanauki.pl/articles/1208176.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Newton and quasi-Newton methods
unconstrained high-dimensional optimization
conjugate gradient methods
Opis:
The conjugate gradient method of Liu and Storey is an efficient minimization algorithm which uses second derivatives information, without saving matrices, by finite difference approximation. It is shown that the finite difference scheme can be removed by using a quasi-Newton approximation for computing a search direction, without loss of convergence. A conjugate gradient method based on BFGS approximation is proposed and compared with existing methods of the same class.
Źródło:
Applicationes Mathematicae; 2000, 27, 2; 153-165
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Kant a Newton (z perspektywy Opus postumum)
Kant and Newton (From the Perspective of Opus Postumum)
Autorzy:
Kupś, Tomasz
Powiązania:
https://bibliotekanauki.pl/articles/423403.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet w Białymstoku. Wydawnictwo Uniwersytetu w Białymstoku
Tematy:
Kant
Newton
progress of science
chemistry
postęp nauki
chemia
Opis:
Kant’s attitude towards Newton is ambiguous though he owes much to him. Although Newton’s physics is a paradigm of science for Kant, he is fully aware that few appearances occur accurately according to the way described by mechanics. When he ties the principles of his philosophy with Newton’s mechanics, Kant makes a mistake, for due to the development of knowledge it began losing its absolute position in science in his day. In Opus postumum Kant recognizes the mistake and no longer refers to the rules of Metaphysische Anfangsgründe der Naturwissenschaft as the ultimate ones. Till the beginning of his work on Opus postumum Newtonian mechanics was a paradigm of science for Kant. It ceases to be so in Opus postumum, where Newton is present mainly as the object of Kant’s polemics. The progress of science, new phenomena, new methods, the development of chemistry. In Metaphysische Anfangsgründe der Naturwissenschaft chemistry was not referred to as science (since it was Newton’s mechanics that was the paradigm of science), whereas in Metaphysik der Sitten (1797) Kant defines Lavoisier’s chemistry as the only chemistry [AA VI 207]; in Anthropologie [AA VII 326] (1798) he ranks Lavoisier as high as Archimedes and Newton. New main problems appeared science which had to deal with: combustibility, origin of acids, the change of the state of matter, electricity, magnetism and – first of all – theory of heat. The main notion of the new theory of chemistry developed by Lavoisier (ether, the caloric) takes the central position also in Kant’s theory of transition (Übergang).
Źródło:
IDEA. Studia nad strukturą i rozwojem pojęć filozoficznych; 2015, 27/t.t.; 203-220
0860-4487
Pojawia się w:
IDEA. Studia nad strukturą i rozwojem pojęć filozoficznych
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Czy Isaac Newton wynalazł napęd odrzutowy
Did Isaac Newton invent jet propulsion technology
Autorzy:
Rodzeń, Jacek
Powiązania:
https://bibliotekanauki.pl/articles/1398805.pdf
Data publikacji:
2018-12-31
Wydawca:
Polska Akademia Nauk. Instytut Historii Nauki im. Ludwika i Aleksandra Birkenmajerów
Tematy:
Isaac Newton
silnik parowy
technika
mit historiograficzny
steam engine
technology
historiographical myth
Opis:
Since the 19th century, both popular and professional literature presented a possibility according to which Isaac Newton contributed to some extent to the invention of jet propulsion. In the presented paper, this view is carefully analysed. Various authors attributed to Newton the design of a road vehicle (the so-called Newton’s steam carriage) moved by ejection of hot steam. This opinion was expressed in certain works written by the first supporters of Newton, e.g. Willem Jacob ’s Gravesande, John Theophilus Desaguliers Desaguliers and Jean Antoine Nollet. What is more, there are miniature models of such a vehicle present in some collections of scientific instruments. Relying on the above examples, it would be hard to prove that Newton was indeed the true inventor of jet propulsion. However, there is no doubt that he was very interested in various engineering issues and invented several scientific instruments, e.g. the variant of a reflecting telescope, a sea octant and a rotary slide rule.
Źródło:
Analecta. Studia i Materiały z Dziejów Nauki; 2018, 27, 2; 115-138
1509-0957
Pojawia się w:
Analecta. Studia i Materiały z Dziejów Nauki
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
W stronę odnowionego wizerunku Newtona
Towards renovated Newtons image
Autorzy:
Rodzeń, Jacek
Powiązania:
https://bibliotekanauki.pl/articles/690868.pdf
Data publikacji:
2019
Wydawca:
Copernicus Center Press
Tematy:
Izaak Newton
Newton as Philosopher
Mathematical Practitioners
natural philosophy
science and religion
geometry and mechanics
Isaac Newton
Opis:
Book review: Niccolò Guicciardini, Isaac Newton and Natural Philosophy, Reaktion Books, London 2018, ss. 268.
Recenzja książki: Niccolò Guicciardini, Isaac Newton and Natural Philosophy, Reaktion Books, London 2018, ss. 268.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2019, 66; 310-316
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Oktant morski Isaaca Newtona
Isaac Newton’s marine octant
Autorzy:
Rodzeń, Jacek
Powiązania:
https://bibliotekanauki.pl/articles/2089504.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
Tematy:
Newton Isaac
octant
navigational instruments in the 17th century
Newton Izaak
oktant
przyrządy nawigacyjne w XVII wieku
Opis:
Isaac Newton is known primarily as an outstanding mathematician and physicist. Less known are his interests in alchemy, theology, and history. Yet, we still know very little about his interest in engineering and about how he designed and created several scientific instruments (e.g. a variant of the reflecting telescope, a variant of the rotary slide rule). Among them, there is also a navigational octant built by Newton in 1699. This device is an example of an ingenious solution in the field of early modern catadioptrical instruments.
Źródło:
Kwartalnik Historii Nauki i Techniki; 2020, 65, 3; 77--94
0023-589X
2657-4020
Pojawia się w:
Kwartalnik Historii Nauki i Techniki
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Newton i teologia naturalna
Newton and Natural Theology
Autorzy:
Schrader, David E.
Powiązania:
https://bibliotekanauki.pl/articles/2015810.pdf
Data publikacji:
2003
Wydawca:
Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
Tematy:
teologia naturalna
Newton
nauki przyrodniczne
Darwin
teoria ewolucji
inteligentny projekt
natural theology
natural sciences
theory of evolution
inteligent design
Opis:
The publication of Sir Isaac Newton's Principia led not only to a revolution in physics, but also gave rise to a new set of directions in natural theology. The mechanistic image of the physical universe that arose from Newton's physics was best explained, according to Newton's contemporaries and followers in the 18th and early 19th centuries, by an appeal to the powerful hand of a wise designing God. Despite critiques by Hume and Kant, that natural theology held broad appeal among scientifically minded people until the work of Charles Darwin proposed a new type of explanatory mechanism that radically undercut the fundamental directions of Newtonian natural theology.
Źródło:
Roczniki Filozoficzne; 2003, 51, 2; 33-45
0035-7685
Pojawia się w:
Roczniki Filozoficzne
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Henry More i Isaac Newton o działaniu materii – kontekst neoplatoński
Henry More and Isaac Newton on the activity of matter – neoplatonic context
Autorzy:
Kucharski, Dariusz
Powiązania:
https://bibliotekanauki.pl/articles/431181.pdf
Data publikacji:
2018
Wydawca:
Uniwersytet Kardynała Stefana Wyszyńskiego w Warszawie
Tematy:
matter
motion
active principles
God
Neoplatonism
alchemy
More Henry
Newton Isaak
materia
ruch
zasady aktywne
Bóg
neoplatonizm
alchemia
Newton Izaak
Opis:
One of the main challenges for 17th-century natural philosophers was to find an answer to the question of what makes matter active at all? The legacy of 'prime matter' and its pure potentiality was still alive, and the adoption of corpuscular or atomistic theories did not change much here, the conviction about the total passivity of bodies was still dominant. Their actions demanded some explanation that would be the equivalent of an Aristotelian, non-material and active form. It seems that one of the philosophical traditions that were sought for such an explanation was the emanational metaphysics of Plotinus. In seventeenth-century systems it underwent various modifications, but its main idea, indicating the active role of certain 'principles' or 'spirits' responsible for initiating any changes in matter and managing them in accordance with the Creator's intention, remained the foundation of the theories of matter. An example of such solutions are the systems of Henry More and his good acquaintance from Cambridge, Isaac Newton. In the first case there is no doubt about the fundamental influence of Neoplatonism, but in the second case historians' opinions are divided. Newton reaches in search of 'active principles' for alchemical research, with the hope of finding these principles not only when referring to philosophical speculations, but also to experimental methods. This difference, however, does not change the fact that both philosophers try to discover the mode of action of 'active spirits', hesitating between placing in the particles of matter a number of separate principles and pointing to only one acting universally principle that was just an extension of God's arm – More calls it the Spirit of Nature (Vicarious Power of God), and Newton sees that principle ultimately in Christ (Viceroy of God).
Jednym z głównych wyzwań stojących przed filozofami przyrody XVII wieku było znalezienie odpowiedzi na pytanie, co sprawia, że materia w ogóle działa? Dziedzictwo ‘materii pierwszej’ i jej czystej potencjalności było wciąż żywe, a przyjęcie teorii korpuskularnej czy atomistycznej niewiele tu zmieniało, dominowało wciąż przekonanie o całkowitej bierności ciał. Ich działanie domagało się jakiegoś wyjaśnienia, które stanowiłoby odpowiednik arystotelesowskiej, niematerialnej i aktywnej, formy. Wydaje się, że jedną z tradycji filozoficznych, do których sięgano w poszukiwaniu takiego wyjaśnienia, była emanacyjna metafizyka Plotyna. W systemach XVII-wiecznych ulegała ona różnorodnym modyfikacjom, ale jej główna idea, wskazująca na aktywną rolę pewnych ‘zasad’, czy ‘duchów’ odpowiedzialnych za inicjowanie wszelkich zmian w materii i kierowanie nimi zgodnie z zamysłem Stwórcy, pozostawała fundamentem ówczesnych teorii działania materii. Przykładem takich rozwiązań są systemy Henry’ego More’a i jego dobrego znajomego z Cambridge, Izaaka Newtona. W pierwszym przypadku nie ma wątpliwości co do zasadniczego wpływu neoplatonizmu, w drugim jednak zdania historyków są podzielone. Newton sięga bowiem w poszukiwaniu ‘aktywnych zasad’ do badań alchemicznych, z nadzieją odnalezienia owych zasad nie tylko przy odwołaniu się do filozoficznych spekulacji, ale także do metod eksperymentalnych. Różnica ta jednak nie zmienia faktu, że obaj filozofowie starają się odkryć sposób działania ‘duchów aktywnych’, wahając się między umieszczeniem w cząstkach materii wielu odrębnych zasad a wskazaniem na zasadę jedną, działającą uniwersalnie i będącą niejako przedłużeniem Bożego ramienia – More nazywa ją Duchem Natury (Vicarious Power of God), a Newton upatruje jej ostatecznie w Chrystusie (Viceroy of God).
Źródło:
Studia Philosophiae Christianae; 2018, 54, 4; 5-26
0585-5470
Pojawia się w:
Studia Philosophiae Christianae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Inexact Newton’s method for generalized operator equations in Banach spaces
Autorzy:
Singh, V. K.
Powiązania:
https://bibliotekanauki.pl/articles/122957.pdf
Data publikacji:
2018
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
nonlinear operator equation
Fréchet derivative
Newton’s method
inexact
Newton method
pochodna Frécheta
metoda Newtona
niedokładna metoda Newtona
Opis:
In the present paper, we introduce a new inexact Newton-like algorithm for solving the generalized operator equations containing non differentiable operators in Banach space setting and discuss its semilocal convergence analysis under the weak Lipschitz condition with larger convergence domain and tighter error bounds. The main result of this paper is the significant improvement over the Newton’s method as well as the inexact Newton method.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 4; 85-97
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Boullee, Wolter, Newton. Architektura i newtonianizm w dobie oświecenia
Boullee, Voltaire, Newton. Architecture and newtonianism in the age of Enlightment
Autorzy:
Świtek, Gabriela
Powiązania:
https://bibliotekanauki.pl/articles/706994.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Boullee
Voltaire
Newton
theory of architecture
Enlightment
Wolter
teoria architektury
oświecenie
Opis:
This article presents selected aspects of the cult of Isaac Newton in France during the Age of the Enlightenment that appear both in Voltaire’s philosophical writings as well as in contemporary visual culture. These reflections feed into art historical interest in the affinity of “two cultures” (C.P. Snow), that is science and humanities, at the same raising questions on methods of research in the reception of scientific theories in art. The paper recalls earlier research on the phenomenon of Newtonianism in eighteenth century European culture (F. Wagner, J.B. Shank), as well as discussions on Newtonian iconography in literature and the visual arts (M.H. Nicholson, M. Keynes, F. Haskell, J. Gage, A.M. Vogt). The celebrated project by Étienne-Louis Boullée for Newton’s cenotaph serves as the main architectural example of Newtonianism in the Age of Enlightenment, but also contributes to analysis on the reception of scientific discoveries in visual arts. The description of Newton’s cenotaph, included in Architecture; Essai sur l’art by Boullée, is compared with selected excerpts from Letters on the English and Elements of Newton’s Philosophy by Voltaire, these being the main source of the popularization of his scientific discoveries in France. The design for Newton’s monument is interpreted in the context of a wider phenomenon, namely the cult of the genius and the cult of posterity in the Enlightenment era. Two aspects of Boullée’s project – the spherical shape and the symbolism of light – are subject to a more detailed analysis, since the decomposition of light and the law of gravity that encompasses the infinite space of the universe are the two main themes recurring in Newton’s iconography, in literature, painting and sculpture. The spherical shape of the cenotaph (as noted earlier by the architect’s monographer A.M. Vogt) is not an “illustration” of Newton’s discovery; the law of gravity assumes that the Earth is not a sphere, but a spheroid. The spherical form of the monument can, at most, be considered as an example of the quest for new formulations of iconography, referring to the attributes of the astronomer and Astronomy (Urania); as one example of the so-called fabriques astronomiques; as a reinterpretation of the shape of the Pantheon; or a reference to then contemporary hot air ballooning. The contrast of light and shadow, mentioned by Boullée in his description of the cenotaph, has little in common with the representation of the famous Newtonian experiment of the dispersive prism. Rather, it forms part of a new and persuasive symbolism of light and darkness, typical of the French Enlightenment, present for example in the depictions of the Apotheosis of Voltaire, as well as in the aesthetics of the sublime outlined by Edmund Burke. The importance of light in Newton’s cenotaph is interpreted in conjunction with the iconography of a small garden building in Ermenonville (Temple de la Philosophie Moderne), in which one column bearing the inscription “Newton – Lucem” was dedicated to the scientist. This context brings us to an earlier analysis of this rotunda (V. Klein), which emphasized that Newton’s achievements – known in France in the second half of the eighteenth century – included not just the decomposition of white light using a prism, but also an early hypothesis defining light as a kind of ether.
Źródło:
Rocznik Historii Sztuki; 2014, 39; 73-96
0080-3472
Pojawia się w:
Rocznik Historii Sztuki
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Engineering interests and inventions of Isaac Newton
Autorzy:
Rodzeń, Jacek
Powiązania:
https://bibliotekanauki.pl/articles/783330.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Umiejętności
Tematy:
Isaac Newton, engineering, scientific instruments, steam engine, history of navigation, 17th century science
Isaac Newton, inżynieria, przyrządy naukowe, maszyna parowa, historia nawigacji, siedemnasty wiek
Opis:
The paper presents engineering interests of Isaac Newton, including some of his technical inventions. So far, this topic has not been studied in a broader manner and in more depth. This article discusses Newton’s youthful passions against the backdrop of the so-called mathematical magic literature. His two inventions, i.e. variants of the reflecting telescope and the marine octant are also discussed. Finally, an example is provided of the involvement of the author of Principia in a discussion around the steam engine and the ship powered by such engine designed by Denis Papin.
Artykuł przedstawia zainteresowania inżynierskie Isaaca Newtona, w tym niektóre z jego wynalazków technicznych. Temat ten nie doczekał się jak dotąd szerszego i pogłębionego opracowania. W artykule poruszono młodzieńcze pasje Newtona na tle literatury z zakresu tzw. magii matematycznej. Omówiono także dwa wynalazki Newtona – wariant teleskopu zwierciadłowego i oktant morski. Na koniec został przytoczony przykład zaangażowania autora Zasad w dyskusję nad projektem technicznym maszyny parowej i napędzanego przez nią statku autorstwa Denisa Papina.
Źródło:
Studia Historiae Scientiarum; 2020, 19
2451-3202
Pojawia się w:
Studia Historiae Scientiarum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Newton numbers and residual measures of plurisubharmonic functions
Autorzy:
Rashkovskii, Alexander
Powiązania:
https://bibliotekanauki.pl/articles/1207853.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Monge-Ampère operator
local indicator
directional Lelong number
plurisubharmonic function
Newton polyhedron
Opis:
We study the masses charged by $(dd^cu)^n$ at isolated singularity points of plurisubharmonic functions u. This is done by means of the local indicators of plurisubharmonic functions introduced in [15]. As a consequence, bounds for the masses are obtained in terms of the directional Lelong numbers of u, and the notion of the Newton number for a holomorphic mapping is extended to arbitrary plurisubharmonic functions. We also describe the local indicator of u as the logarithmic tangent to u.
Źródło:
Annales Polonici Mathematici; 2000, 75, 3; 213-231
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Krótka historia Principiów Newtona
A Short History of Newton’s Principia
Autorzy:
Pabjan, Tadeusz
Powiązania:
https://bibliotekanauki.pl/articles/691280.pdf
Data publikacji:
2012
Wydawca:
Copernicus Center Press
Tematy:
history of science
Isaack Newton
Philosophiae Naturalis Principia Mathematica
Opis:
The Polish translation of the most famous treatise of Newton has just been published, which is a good opportunity to recall some of the episodes related to the origin of Principia. In the first part of this three piece paper, the historical context is presented, in which unsolved scientific problems – specially those of planetary motions – were discussed before Newton; in the second part, the circumstances of the process of the writing of the Principia are outlined; in the third part, some facts are recalled which show that not all scientists and philosophers at once recognized the value and the importance of Newton’s treatise. Finally, some remarks on the Polish edition are made.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2012, 50; 102-117
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Wyzwanie dla racjonalności: Leibniz i początek ery Newtona
Rationality at Stake: Leibniz and the Beginnings of Newton’s Era
Autorzy:
Heller, Michał
Powiązania:
https://bibliotekanauki.pl/articles/690808.pdf
Data publikacji:
2016
Wydawca:
Copernicus Center Press
Tematy:
rationality
empiricism
Leibniz’s philosophy
Newton’s methodology
philosophy of science
Gottfried Wilhelm Leibniz
Isaack Newton
Opis:
Our present knowledge in the field of dynamical systems, information theory, probability theory and other similar domains indicates that the human brain is a complex dynamical system working in a strong chaotic regime in which random processes play important roles. In this environment our mental life develops. To choose a logically ordered sequence from a random or almost random stream of thoughts is a difficult and energy consuming task. The only domain in which we are able to do this with a full success is mathematics. Leibniz’s life ambition was to extend this success, with the help of what he called characteristica universalis, to other areas of human activity. The belief that this is possible lies at the basis of Leibniz’s rationalist system. Reasoning within his system, Leibniz claimed that also fundamental laws of physics can be deduced from the “first principles”. Just as linguistic or conceptual units are at the basis of the charactersistica universalis, his monads are responsible for physical activity of material bodies. When this rationalistic strategy is applied to the philosophy of space and time, it leads to their radically relational conception. Leibniz’s rationalistic approach to philosophy and science arouses out sympathy but it was Newton’s mathematical-empirical method that turned out to be effective in human endeavour to understand the functioning of the physical world. Successes of the Newtonian method  compel us to revise our concept of rationality.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2016, 61; 5-22
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Adaptive Newton-like method for shape optimization
Autorzy:
Roche, J. R.
Powiązania:
https://bibliotekanauki.pl/articles/970159.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optymalizacja kształtu
zdolność przystosowania się
shape optimization
Newton-like algorithm
posteriori error
adaptability
Opis:
The aim of this work is to introduce an adaptive strategy to monitor the rate of convergence of a Newton-like method in numerical shape optimization. Such superlinear iterative algorithms are often computationally intensive and the rate of convergence depends on how accurate the numerical solution of the state equation is. The model concerns a cost function depending on the unknown domain [Omega], and the solution of an integral equation.
Źródło:
Control and Cybernetics; 2005, 34, 1; 363-377
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized Newton and NCP-methods: convergence, regularity, actions
Autorzy:
Kummer, Bernd
Powiązania:
https://bibliotekanauki.pl/articles/729371.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
nonsmooth functions
generalized Newton methods
critical points
complementarity
SQP methods
inverse mappings
regularity
Opis:
Solutions of several problems can be modelled as solutions of nonsmooth equations. Then, Newton-type methods for solving such equations induce particular iteration steps (actions) and regularity requirements in the original problems. We study these actions and requirements for nonlinear complementarity problems (NCP's) and Karush-Kuhn-Tucker systems (KKT) of optimization models. We demonstrate their dependence on the applied Newton techniques and the corresponding reformulations. In this way, connections to SQP-methods, to penalty-barrier methods and to general properties of so-called NCP-functions are shown. Moreover, direct comparisons of the hypotheses and actions in terms of the original problems become possible. Besides, we point out the possibilities and bounds of such methods in dependence of smoothness.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2000, 20, 2; 209-244
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Branched coverings and cubic Newton maps
Autorzy:
Tan, Lei
Powiązania:
https://bibliotekanauki.pl/articles/1205408.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:
We construct branched coverings such as matings and captures to describe the dynamics of every critically finite cubic Newton map. This gives a combinatorial model of the set of cubic Newton maps as the gluing of a subset of cubic polynomials with a part of the filled Julia set of a specific polynomial (Figure 1).
Źródło:
Fundamenta Mathematicae; 1997, 154, 3; 207-260
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The effect of rounding errors on a certain class of iterative methods
Autorzy:
Argyros, Ioannis
Powiązania:
https://bibliotekanauki.pl/articles/1208172.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Fréchet derivative
Lipschitz conditions
Newton-like method
inexact Newton-like method
Banach space
Opis:
In this study we are concerned with the problem of approximating a solution of a nonlinear equation in Banach space using Newton-like methods. Due to rounding errors the sequence of iterates generated on a computer differs from the sequence produced in theory. Using Lipschitz-type hypotheses on the mth Fréchet derivative (m ≥ 2 an integer) instead of the first one, we provide sufficient convergence conditions for the inexact Newton-like method that is actually generated on the computer. Moreover, we show that the ratio of convergence improves under our conditions. Furthermore, we provide a wider choice of initial guesses than before. Finally, a numerical example is provided to show that our results compare favorably with earlier ones.
Źródło:
Applicationes Mathematicae; 2000, 27, 3; 369-375
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
‘We Make Ourselves at Home Wherever We are’1-Older Peoples Placemaking in Newton Hall
Autorzy:
van Hoven, Bettina
Douma, Linden
Powiązania:
https://bibliotekanauki.pl/articles/623609.pdf
Data publikacji:
2012-07-26
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
ageing
older people
place attachment
Newton Hall
Opis:
The aim of this paper is to explore older in-migrants' experiences and perceptions of their spatial context at the neighbourhood level, the key aspects in their attachment to the neighbourhood, and the role of place in their experience of ageing. Our qualitative research was carried out in Newton Hall (United Kingdom). The findings show that older people can have a proactive role in terms of placemaking and their own wellbeing. However, the study also reveals that the condition of the spatial context can either support or hinder older people's sense of wellbeing.
Źródło:
European Spatial Research and Policy; 2012, 19, 1
1231-1952
1896-1525
Pojawia się w:
European Spatial Research and Policy
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Efficiency and Convergence of Bisection, Secant, and Newton Raphson Methods in Estimating Implied Volatility
Autorzy:
Mahrudinda, Mahrudinda
Munandar, Devi
Purwani, Sri
Powiązania:
https://bibliotekanauki.pl/articles/1193324.pdf
Data publikacji:
2021
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Black-Scholes model
Newton Raphson
bisection
secant
volatility
volatility implied
Opis:
This study aims to estimate volatility prices based on the black-Scholes model (BSM) function with research data taken during the COVID-19 pandemic. The estimates of the volatility values are obtained by using three numerical methods, namely the bisection, secant, and Newton Raphson methods. The numerical processes that produce some iteration results in the three methods are then analyzed and the best convergence is sought. As a result, Newton Raphson method produces the smallest number of iterations, which stops at the 3rd iteration and gets a volatility value of 0.500451 with an absolute error value of 0.000388. However, the method requires an initial approximation which lies only in two intervals on the axis σ which are close to the true root. Meanwhile, for the other two methods, namely Bisection and Secant, this limitation does not apply, as long as there is an interval that guarantees the existence of roots. In this case, bisection method requires11 iterations to converge with volatility value of 0.500342 and error value of 0.000878. Whereas secant method requires 4 iterations to converge with a volatility value of 0.500449 and error value of 1.68938E-05. This suggests, that in some cases the use of Newton method, should be initialized with the use of bisection or secant method, to ensure successful iteration and accelerate the rate of convergence.
Źródło:
World Scientific News; 2021, 153, 2; 157-168
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Convergence of the Lagrange-Newton Method for Optimal Control Problems
Autorzy:
Malanowski, K. D.
Powiązania:
https://bibliotekanauki.pl/articles/907971.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
sterowanie optymalne
ograniczenia mieszane
metoda Lagrange'a-Newtona
optimal control
nonlinear ODEs
mixed constraints
Lagrange-Newton method
Opis:
Convergence results for two Lagrange-Newton-type methods of solving optimal control problems are presented. It is shown how the methods can be applied to a class of optimal control problems for nonlinear ODEs, subject to mixed control-state constraints. The first method reduces to an SQP algorithm. It does not require any information on the structure of the optimal solution. The other one is the shooting method, where information on the structure of the optimal solution is exploited. In each case, conditions for well-posedness and local quadratic convergence are given. The scope of applicability is briefly discussed.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2004, 14, 4; 531-540
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Predicting in multivariate incomplete time series. Application of the expectation-maximisation algorithm supplemented by the Newton-Raphson method
Autorzy:
Korczyński, Adam
Powiązania:
https://bibliotekanauki.pl/articles/1806793.pdf
Data publikacji:
2021-08-24
Wydawca:
Główny Urząd Statystyczny
Tematy:
missing data
multivariate time series
expectation-maximisation algorithm
Newton-Raphson algorithm
Opis:
Statistical practice requires various imperfections resulting from the nature of data to be addressed. Data containing different types of measurement errors and irregularities, such as missing observations, have to be modelled. The study presented in the paper concerns the application of the expectation-maximisation (EM) algorithm to calculate maximum likelihood estimates, using an autoregressive model as an example. The model allows describing a process observed only through measurements with certain level of precision and through more than one data series. The studied series are affected by a measurement error and interrupted in some time periods, which causes the information for parameters estimation and later for prediction to be less precise. The presented technique aims to compensate for missing data in time series. The missing data appear in the form of breaks in the source of the signal. The adjustment has been performed by the EM algorithm to a hybrid version, supplemented by the Newton-Raphson method. This technique allows the estimation of more complex models. The formulation of the substantive model of an autoregressive process affected by noise is outlined, as well as the adjustment introduced to overcome the issue of missing data. The extended version of the algorithm has been verified using sampled data from a model serving as an example for the examined process. The verification demonstrated that the joint EM and Newton-Raphson algorithms converged with a relatively small number of iterations and resulted in the restoration of the information lost due to missing data, providing more accurate predictions than the original algorithm. The study also features an example of the application of the supplemented algorithm to some empirical data (in the calculation of a forecasted demand for newspapers).
Źródło:
Przegląd Statystyczny; 2021, 68, 1; 17-46
0033-2372
Pojawia się w:
Przegląd Statystyczny
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Local convergence of inexact Newton methods under affine invariant conditions and hypotheses on the second Fréchet derivative
Autorzy:
Argyros, Ioannis
Powiązania:
https://bibliotekanauki.pl/articles/1338691.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
superlinear
Fréchet derivative
weak convergence
inexact Newton method
strong
forcing sequence
Banach space
Opis:
We use inexact Newton iterates to approximate a solution of a nonlinear equation in a Banach space. Solving a nonlinear equation using Newton iterates at each stage is very expensive in general. That is why we consider inexact Newton methods, where the Newton equations are solved only approximately, and in some unspecified manner. In earlier works [2], [3], natural assumptions under which the forcing sequences are uniformly less than one were given based on the second Fréchet derivative of the operator involved. This approach showed that the upper error bounds on the distances involved are smaller compared with the corresponding ones using hypotheses on the first Fréchet derivative. However, the conditions on the forcing sequences were not given in affine invariant form. The advantages of using conditions given in affine invariant form were explained in [3], [10]. Here we reproduce all the results obtained in [3] but using affine invariant conditions.
Źródło:
Applicationes Mathematicae; 1999, 26, 4; 457-465
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-25 z 120

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