Temat: Lipschitz - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Point derivations for Lipschitz functions andClarkes generalized derivative
Autorzy:: Demyanov, Vladimir
Pallaschke, Diethard
Powiązania:: https://bibliotekanauki.pl/articles/1339173.pdf
Data publikacji:: 1997
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: point derivations
generalized directional derivative
Lipschitz functions
Opis:: Clarke's generalized derivative $f^0(x,v)$ is studied as a function on the Banach algebra Lip(X,d) of bounded Lipschitz functions f defined on an open subset X of a normed vector space E. For fixed $x\in X$ and fixed $v\in E$ the function $f^0(x,v)$ is continuous and sublinear in $f\in Lip(X,d)$. It is shown that all linear functionals in the support set of this continuous sublinear function satisfy Leibniz's product rule and are thus point derivations. A characterization of the support set in terms of point derivations is given.
Źródło:: Applicationes Mathematicae; 1996-1997, 24, 4; 465-474
1233-7234
Pojawia się w:: Applicationes Mathematicae
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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