Temat: Lipschitz - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Generalized trend constants of Lipschitz mappings
Autorzy:: Szczepanik, Mariusz
Powiązania:: https://bibliotekanauki.pl/articles/747268.pdf
Data publikacji:: 2018
Wydawca:: Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:: Banach space
Lipschitz mapping
fixed point
Opis:: In 2015, Goebel and Bolibok defined the initial trend coefficient of a mapping and the class of initially nonexpansive mappings. They proved that the fixed point property for nonexpansive mappings implies the fixed point property for initially nonexpansive mappings. We generalize the above concepts and prove an analogous fixed point theorem. We also study the initial trend coefficient more deeply.
Źródło:: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2018, 72, 2
0365-1029
2083-7402
Pojawia się w:: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: A new Kantorovich-type theorem for Newtons method
Autorzy:: Argyros, Ioannis
Powiązania:: https://bibliotekanauki.pl/articles/1338842.pdf
Data publikacji:: 1999
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: Newton's method
Lipschitz-Hölder condition
Kantorovich hypothesis
Banach space
Opis:: A new Kantorovich-type convergence theorem for Newton's method is established for approximating a locally unique solution of an equation F(x)=0 defined on a Banach space. It is assumed that the operator F is twice Fréchet differentiable, and that F', F'' satisfy Lipschitz conditions. Our convergence condition differs from earlier ones and therefore it has theoretical and practical value.
Źródło:: Applicationes Mathematicae; 1999, 26, 2; 151-157
1233-7234
Pojawia się w:: Applicationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

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

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