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    Wyświetlanie 1-14 z 14
    Tytuł:
    Local error structures and order conditions in terms of Lie elements for exponential splitting schemes
    Autorzy:
    Auzinger, W.
    Herfort, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/255869.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    exponential splitting schemes
    local error
    defect
    order conditions
    free Lie algebra
    Opis:
    We discuss the structure of the local error of exponential operator splitting methods. In particular, it is shown that the leading error term is a Lie element, i.e., a linear combination of higher-degree commutators of the given operators. This structural assertion can be used to formulate a simple algorithm for the automatic generation of a minimal set of polynomial equations representing the order conditions, for the general case as well as in symmetric settings.
    Źródło:
    Opuscula Mathematica; 2014, 34, 2; 243-256
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A local truncation error estimation for a SubIval solver
    Autorzy:
    Sowa, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/202058.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional calculus
    numerical method
    adaptive step size
    local truncation error
    circuit analysis
    rachunek różniczkowy
    metoda numeryczna
    analiza obwodów
    Opis:
    The paper concerns an analysis for SubIval (the subinterval-based method for fractional derivative computations in initial value problems). A time step size adaptive solver is discussed, for which the formula of a local truncation error is derived. A general form for a system of linear equations is given for the considered class of problems (for which the analysis is performed in the paper). Two circuit examples are introduced to display the usefulness of the SubIval solver. For the examples that have been chosen it is possible to obtain referential solutions through completely different methods. The results obtained through the numerical solver are compared with evaluations of the referential solutions. The error estimation results obtained for the time steps of the SubIval solver are compared with the actual errors, being the differences between the numerical solutions and the referential solutions. The paper also contains a comparison of the accuracy of results obtained through the SubIval solver with the accuracies of other solvers.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 475-484
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Methods of Step-Size Distribution Optimization Used in S-SSFM Simulations of WDM Systems
    Autorzy:
    Jaworski, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/308958.pdf
    Data publikacji:
    2009
    Wydawca:
    Instytut Łączności - Państwowy Instytut Badawczy
    Tematy:
    local error method
    logarithmic step
    simulation
    split-step Fourier method
    WDM
    Opis:
    Brief review of methods used for simulation of signal propagation in wavelength division multiplexed (WDM)links is presented. We propose two novel methods of stepsize distribution optimization used to improve symmetrized split step Fourier method (S-SSFM) numerical efficiency: presimulated local error S-SSFM (PsLE S-SSFM) and modified logarithmic (ML S-SSFM). The PsLE S-SSFM contains two stages: in the initial stage step-size distribution optimization is carried out by combining local error method and presimulation with signal spectrum averaging; in the second stage conventional SSFM is used by applying optimal step-size distribution obtained in the initial stage. The ML S-SSFMis generalization of logarithmic method proposed to suppress spurious FWM tones, in which a slope of logarithmic step-size distribution is optimized. Overall time savings exceed 50%, depending of a simulated system scenario.
    Źródło:
    Journal of Telecommunications and Information Technology; 2009, 1; 44-50
    1509-4553
    1899-8852
    Pojawia się w:
    Journal of Telecommunications and Information Technology
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A new nonlinear L-stable scheme with constant and adaptive step-size strategy
    Autorzy:
    Arain, Sadia
    Qureshi, Sania
    Shaikh, Asif Ali
    Powiązania:
    https://bibliotekanauki.pl/articles/2175496.pdf
    Data publikacji:
    2021
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    stiff systems
    singular systems
    L-stability
    local error
    order stars
    systemy sztywne
    układ singularny
    stabilność L
    błąd lokalny
    Opis:
    The present study proposes a new explicit nonlinear scheme that solves stiff and nonlinear initial value problems in ordinary differential equations. One of the promising features of this scheme is its fourth-order convergence with strong stability having an unbounded region. A modern approach for relative stability growth analysis is also presented under order stars conditions. The scheme is also good in dealing with singular and stiff type of models. Comparing numerical experiments using various errors, including maximum absolute global error over the integration interval, absolute error at the endpoint, average error, norm of errors, and the CPU times (seconds), shows better performance. An adaptive step-size approach seems to increase the performance of the proposed scheme. The numerical simulations assure us of L -stability, consistency, order, and rapid convergence.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 4; 7--18
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Local accuracy and error bounds of the improved Runge-Kutta numerical methods
    Autorzy:
    Qureshi, S.
    Memon, Z.
    Shaikh, A. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/122862.pdf
    Data publikacji:
    2018
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    error estimate
    remainder term
    principal error function
    truncation error
    Lotkin bound
    granice błędu
    metoda numeryczna Runge-Kutty
    błąd obcięcia
    granica Lotkina
    funkcja błędu
    szacowanie błędu
    Opis:
    In this paper, explicit Improved Runge-Kutta (IRK) methods with two, three and four stages have been analyzed in detail to derive the error estimates inherent in them whereas their convergence, order of local accuracy, stability and arithmetic complexity have been proved in the relevant literature. Using single and multivariate Taylor series expansion for a mathematical function of one and two variables respectively, slopes involved in the IRK methods have been expanded in order to obtain the general expression for the leading or principal term in the local truncation error of the methods. In addition to this, principal error functions of the methods have also been derived using the idea of Lotkin bounds which consequently gave rise to the error estimates for the IRK methods. Later, these error estimates were compared with error estimates of the two, three, and four-stage standard explicit Runge-Kutta (RK) methods to show the better performance of the IRK methods in terms of the error bounds on the constant step-size h used for solving the initial value problems in ordinary differential equations. Finally, a couple of initial value problems have been tested to determine the maximum absolute global errors, absolute errors at the final nodal point of the integration interval and the CPU times (seconds) for all the methods under consideration to get a better idea of how the methods behave in a particular situation especially when it comes to analyzing the error terms.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 4; 73-84
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Use of partial derivatives to derive a convergent numerical scheme with its error estimates
    Autorzy:
    Qureshi, Sania
    Adeyeye, Oluwaseun
    Shaikh, Asif Ali
    Powiązania:
    https://bibliotekanauki.pl/articles/122734.pdf
    Data publikacji:
    2019
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    multi-derivative
    local truncation error
    stability
    absolute relative errors
    consistency
    principal term
    wielopochodna
    pochodna cząstkowa
    schemat numeryczny
    błąd względny
    błąd bezwzględny
    Opis:
    Using the idea of the partial derivative with respect to the ordinate of a given mathematical function, a new numerical scheme having third order convergence has been devised for solving initial value problems in ordinary differential equations. Such problems are deemed to be indispensable in diverse fields of science, medical and engineering and are most often required to be solved by the numerical schemes. In view of this, the proposed numerical scheme is found to be efficient in solving both autonomous and non-autonomous type of problems as supported by some numerical experiments in the present study. Using the Taylor expansion for the slopes involved in the scheme, the leading term of the local truncation error is shown to have contained Ϭ(h4) which proves third order accuracy of the scheme. In addition to this, consistency and linear stability analysis of the proposed scheme has extensively been discussed. Numerical experiments show better performance of the proposed numerical scheme when compared with existing numerical schemes of the same order as that of the scheme proposed. CPU time (seconds), maximum absolute relative error and the absolute relative error, computed at the last grid point of the integration interval for the associated initial value problem, are the parameters to test the performance of the proposed numerical scheme. MATLAB Version: 9.4.0.813654 (R2018a) in double-precision on a personal computer equipped with a Processor Intel (R) Core(TM) i3-4500U CPU@ 1.70 GHz running under the Windows 10 operating system has been employed in order to carry out all the required numerical computations.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 4; 73-83
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Effect of the gear local damage and profile error of the gear on the drivetrain dynamic response
    Autorzy:
    Ghorbel, A.
    Zghal, B.
    Abdennadher, M.
    Walha, L.
    Haddar, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/280233.pdf
    Data publikacji:
    2018
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    dynamic behaviour
    clutch
    gear
    brake disc
    gear local damage
    gear profile error
    Opis:
    The dynamic modeling of vibration of a drivetrain is used for increasing our information about vibration generating mechanisms, especially in the presence of some kind of gear faults. This paper describes a research work on the automotive driveline modeling, vibration analysis, and the effect of gear defects on the dynamic behavior of the system. Firstly, main drivetrain components including the engine, clutch, single stage spur gearbox and disc brake are modeled, respectively. The nonlinear dynamic model is simulated by a thirteen degrees of freedom (DOF) system and the nonlinear function is due to the dry friction path. Secondly, two types of defects are modeled and introduced into the spur gear system; local damage and profile error. Then, the nonlinear equations of motion are solved by the numerical Runge Kutta method and a comparative study of the dynamic behavior of the system in healthy and defected cases is discussed for each fault type. The influence of the defects on the vibration response is presented in the time and frequency domain. Finally, analysis of the two defects together is presented.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2018, 56, 3; 765-779
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Application of local bidirectional language model to error correction in polish medical speech recognition
    Autorzy:
    Sas, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/333597.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Śląski. Wydział Informatyki i Nauki o Materiałach. Instytut Informatyki. Zakład Systemów Komputerowych
    Tematy:
    rozpoznawanie mowy
    modele języka
    medyczne systemy informacji
    speech recognition
    language models
    medical information systems
    Opis:
    In the paper, the method of short word deletion errors correction in automatic speech recognition is described. Short word deletion errors appear to be a frequent error type in Polish speech recognition. The proposed speech recognition process consists of two stages. At the first stage the utterance is recognized by a typical speech recognizer based on forward bigram language model. At the second stage the word sequence recognized by the first stage recognizer is analyzed and such pairs of adjacent words in the recognized sequence are localized, which are likely to be separated by a short word like conjunction or preposition. The probability of short word appearance in context of found words is evaluated using centered trigrams and backward bigram language model for short words prone to deletion. The set of probabilistic language properties used to correct deletions is called here Local Bidirectional Language Model (in contrast to purely forward or backward model used typically in speech recognition). The decision of short word insertion is based on comparison of deletion error probability of the first stage recognizer and the error probability of the decision based only on centered trigrams and backward model. Despite its simplicity, the method proved to be effective in correcting deletion errors of most frequently appearing Polish prepositions. The method was tested in application to medical spoken reports recognition, where the overall short word deletion error rate was reduced by almost 45%.
    Źródło:
    Journal of Medical Informatics & Technologies; 2010, 15; 127-134
    1642-6037
    Pojawia się w:
    Journal of Medical Informatics & Technologies
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Estimation of Measurement Error Using Local Sampling and Joint Nonparametric Linearisation
    Estymowanie błędu pomiarowego z zastosowaniem łącznej nieparametrycznej linearyzacji prób lokalnych
    Autorzy:
    Górkiewicz, Maciej
    Powiązania:
    https://bibliotekanauki.pl/articles/906540.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    local sampling
    linearisation
    measurement error
    neear neighbours
    Opis:
    This paper presents how to use the near neighbours technique in aim to transform a given data set (Z, X, YT) of size N into a set of J ~ N local samples (Z, X), with restrictions on minimal number К of members in each local sample and on maximal difference of Y inside each local sample, where Z plays role of an outcome, X is an independent variable, and Y1 - (Y ..., YL) is a vector of L supplementary continuous variables. Then the procedure for non-parametric joint linearisation of an obtained set of local samples was proposed. The whole proposed method was applied to estimation of models with standard deviation of measurements as outcome Z and measured value as independent variable X. The paper was inspired by difficulties with estimation of the measurement error, which often occur in medicine, if accuracy of a measurement procedure depends on some properties of patient. Nevertheless, the proposed approach seems to be more general. It can be useful in many analyses of observational studies, which aim to estimate a family of the functions, preferable the linear ones, instead a single multivariate model.
    Praca prezentuje zastosowanie techniki najbliższych sąsiadów w celu przekształcenia zbioru N danych postaci (Z, X, YT) w zbiór J ~ N prób lokalnych (Z, X), przy ograniczeniach dotyczących minimalnej liczby danych К oraz różnic wartości YT w każdej próbie lokalnej, gdzie Z pełni rolę zmiennej zależnej, X - zmiennej niezależnej, a Y1 = (Y, ..., YL) jest L-wymiarową zmienną dodatkową. Następnie proponuje się procedurę nieparametrycznej łącznej linearyzacji zbioru prób lokalnych. Obie procedury proponuje się stosować do oceny dokładności metod pomiarowych, z odchyleniem standardowym błędu pomiarów jako zmienną Z i wielkością mierzoną jako zmienną X. Proponowane podejście może być użyteczne w innych zastosowaniach, kiedy zamiast modelu regresji wielowymiarowej estymuje się rodzinę zależności regresyjnych.
    Źródło:
    Acta Universitatis Lodziensis. Folia Oeconomica; 2002, 162
    0208-6018
    2353-7663
    Pojawia się w:
    Acta Universitatis Lodziensis. Folia Oeconomica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Influence of mesh refinement on results of elastic-plastic FEM analysis
    Autorzy:
    Szabracki, P.
    Lipiński, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/297864.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Warmińsko-Mazurski w Olsztynie
    Tematy:
    FEM analysis
    local mesh refinement
    elastic-plastic deformation
    error optimization
    Opis:
    To improve fitting of numerical results to experimental data, in the past, distances between nodes were decreased for whole mesh. A typical mesh generator for Finite Element Method (FEM) analysis ensures possibility to decrease distances between nodes for edges or surfaces of described geometries. Influence of local mesh refinement for a flat and round tensile specimen on fitting of numerical tensile simulation results to experimental data was presented in the paper. Local mesh refinement was performed for areas with the error values higher than threshold value. First iteration of flat and round mesh refinement has to improved correlation of numerical and experimental data with acceptable increase of mesh file size. Similar observations have been made for the second iteration of the flat specimen mesh. On the basis of analysis, shown that second iteration of round mesh refinement caused crucial increase of mesh file size and computation time with negligible fitting improvement.
    Źródło:
    Technical Sciences / University of Warmia and Mazury in Olsztyn; 2014, 17(2); 149-163
    1505-4675
    2083-4527
    Pojawia się w:
    Technical Sciences / University of Warmia and Mazury in Olsztyn
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Local cone approximations in optimization
    Autorzy:
    Castellani, M.
    Pappalardo, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/970281.pdf
    Data publikacji:
    2007
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    nonsmooth optimization
    cone approximations
    generalized directional epiderivatives
    optimality conditions
    constraint qualifications
    mean value theorem
    error bound
    Opis:
    We show how to use intensively local cone approximations to obtain results in some fields of optimization theory such as optimality conditions, constraint qualifications, mean value theorems and error bound.
    Źródło:
    Control and Cybernetics; 2007, 36, 3; 583-600
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Performance of variance function estimators for autoregressive time series of order one: asymptotic normality and numerical study
    Autorzy:
    Borkowski, P.
    Mielniczuk, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/206217.pdf
    Data publikacji:
    2012
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    autoregressive process
    bandwidth
    heteroscedasticity
    integrated squared error
    local linear and local maximum likelihood estimator
    difference-based estimator
    geometric moment contraction
    variance function
    volatility
    Opis:
    We study performance of several conditional variance estimators for an autoregressive time series which include local linear smoothers with various bandwidths, local likelihood and difference-based estimators. In the theoretical part, asymptotic normality of the local linear estimator of variance with no mixing assumptions imposed on the underlying process is proved. Moreover, numerical examples performed reveal that a two-stage local linear smoother with a bandwidth, proposed by Ruppert, Sheather and Wand, used to estimate the regression function and a simple rule of thumb bandwidth for variance estimation performs best for variances without much structure, whereas the bandwidth considered by Fan and Yao works very well for much more variable variances.
    Źródło:
    Control and Cybernetics; 2012, 41, 2; 415-441
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Strong consistency of the local linear relative regression estimator for censored data
    Autorzy:
    Bouhadjera, Feriel
    Saïd, Elias Ould
    Powiązania:
    https://bibliotekanauki.pl/articles/29519178.pdf
    Data publikacji:
    2022
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    censored data
    local linear approach
    relative error
    regression function
    uniform almost sure convergence
    Opis:
    In this paper, we combine the local linear approach to the relative error regression estimation method to build a new estimator of the regression operator when the response variable is subject to random right censoring. We establish the uniform almost sure consistency with rate over a compact set of the proposed estimator. Numerical studies, firstly on simulated data, then on a real data set concerning the death times of kidney transplant patients, were conducted. These practical studies clearly show the superiority of the new estimator compared to competitive estimators.
    Źródło:
    Opuscula Mathematica; 2022, 42, 6; 805-832
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Wybrane aspekty tekstów jednolitych samorządowych aktów prawa miejscowego
    Selected aspects of texts of the self-governmental consolidated statues of local law
    Autorzy:
    Lewicki, Marek
    Powiązania:
    https://bibliotekanauki.pl/articles/685848.pdf
    Data publikacji:
    2016
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    tekst jednolity
    sprostowanie błędu
    prawo miejscowe
    zasady techniki prawodawczej
    zmiana aktu normatywnego
    consolidated text
    correction of an error
    local law
    principles of the legislative technique
    an amendment to a statute
    Opis:
    Practice of amending many times a statute gives rise to some problems in establishing binding contents of the statute. These problems should be eliminated by an institution of a consolidated text. This paper focuses on selected aspects of this legal institution with respect to statutes of local law. It explains regulations normalizing an obligation to announce these texts, their legal character as well as principles of eliminating errors occurring in them . It also emphasizes a necessity of due diligence when editing these texts in order to prevent consolidated texts from being against the binding law.
    Praktyka wielokrotnego nowelizowania aktu normatywnego rodzi problemy w ustaleniu obowiązującej treści tego aktu. Problemy te eliminować ma instytucja tekstu jednolitego. Niniejsze opracowanie poświęcone zostało wybranym aspektom tej instytucji prawnej w odniesieniu do aktów prawa miejscowego. Przybliża ono regulacje normujące obowiązek ogłaszania tych tekstów, ich charakter prawny, a także zasady eliminowania zaistniałych w nich błędów. Podkreśla się również konieczność dokładania najwyższej staranności przy ich redagowaniu w celu zapobieżenia pojawiania się w obrocie prawnym tekstów jednolitych niezgodnych z obowiązującym stanem prawnym.
    Źródło:
    Acta Universitatis Lodziensis. Folia Iuridica; 2016, 77
    0208-6069
    2450-2782
    Pojawia się w:
    Acta Universitatis Lodziensis. Folia Iuridica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-14 z 14

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