A Generalization of Newton's Method PDF Download
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Author: Billy Ruth LeBouf
Publisher:
ISBN:
Category : Equations, Roots of
Languages : en
Pages : 38
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Book Description
Author: Billy Ruth LeBouf
Publisher:
ISBN:
Category : Equations, Roots of
Languages : en
Pages : 38
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Book Description
Author: Richar Alfred Tapia
Publisher:
ISBN:
Category :
Languages : en
Pages : 97
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Book Description
Author: Richard A. Tapia
Publisher:
ISBN:
Category : Calculus of variations
Languages : en
Pages : 106
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Book Description
The paper presents a procedure for approximating the zeros of a nonlinear operator P from a Banach space X to a Banach space Y. This procedure is general enough to include the generalized Euler-Lagrange equation. The procedure presented is called the weak Newton method and is a generalization of L.V. Kantorovish's Newton's method.
Author: Richard W. Cottle
Publisher: SIAM
ISBN: 0898716861
Category : Mathematics
Languages : en
Pages : 781
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Book Description
A revised edition of the standard reference on the linear complementarity problem.
Author: William L. Harper
Publisher: Oxford University Press
ISBN: 019957040X
Category : Philosophy
Languages : en
Pages : 443
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Book Description
Includes bibliographical references (p. [397]-410) and index.
Author: Youssef Benadada
Publisher:
ISBN:
Category : Convergence
Languages : en
Pages : 8
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Book Description
Abstract: "We analyze the convergence of a generalization of Newton's method for finding the root of the equation [Theta](t) = 0 in the case where [Theta] is monotone, convex but not differentiable. We prove that the convergence is superlinear and only superlinear. Indeed for all [alpha] [in] (1,2), we exhibit an example where the convergence of the iterates is exactly [alpha].
Author: José Antonio Ezquerro Fernández
Publisher: Birkhäuser
ISBN: 3319559761
Category : Mathematics
Languages : en
Pages : 175
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Book Description
This book shows the importance of studying semilocal convergence in iterative methods through Newton's method and addresses the most important aspects of the Kantorovich's theory including implicated studies. Kantorovich's theory for Newton's method used techniques of functional analysis to prove the semilocal convergence of the method by means of the well-known majorant principle. To gain a deeper understanding of these techniques the authors return to the beginning and present a deep-detailed approach of Kantorovich's theory for Newton's method, where they include old results, for a historical perspective and for comparisons with new results, refine old results, and prove their most relevant results, where alternative approaches leading to new sufficient semilocal convergence criteria for Newton's method are given. The book contains many numerical examples involving nonlinear integral equations, two boundary value problems and systems of nonlinear equations related to numerous physical phenomena. The book is addressed to researchers in computational sciences, in general, and in approximation of solutions of nonlinear problems, in particular.
Author: Norman Harold Josephy
Publisher:
ISBN:
Category : Nonlinear programming
Languages : en
Pages : 226
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Book Description
Author: Michael Luttenberger
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: Diethard Klatte
Publisher: Springer Science & Business Media
ISBN: 0306476169
Category : Mathematics
Languages : en
Pages : 351
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Book Description
Many questions dealing with solvability, stability and solution methods for va- ational inequalities or equilibrium, optimization and complementarity problems lead to the analysis of certain (perturbed) equations. This often requires a - formulation of the initial model being under consideration. Due to the specific of the original problem, the resulting equation is usually either not differ- tiable (even if the data of the original model are smooth), or it does not satisfy the assumptions of the classical implicit function theorem. This phenomenon is the main reason why a considerable analytical inst- ment dealing with generalized equations (i.e., with finding zeros of multivalued mappings) and nonsmooth equations (i.e., the defining functions are not c- tinuously differentiable) has been developed during the last 20 years, and that under very different viewpoints and assumptions. In this theory, the classical hypotheses of convex analysis, in particular, monotonicity and convexity, have been weakened or dropped, and the scope of possible applications seems to be quite large. Briefly, this discipline is often called nonsmooth analysis, sometimes also variational analysis. Our book fits into this discipline, however, our main intention is to develop the analytical theory in close connection with the needs of applications in optimization and related subjects. Main Topics of the Book 1. Extended analysis of Lipschitz functions and their generalized derivatives, including ”Newton maps” and regularity of multivalued mappings. 2. Principle of successive approximation under metric regularity and its - plication to implicit functions.
