Point Estimation of Root Finding Methods

This book sets out to state computationally verifiable initial conditions for predicting the immediate appearance of the guaranteed and fast convergence of iterative root finding methods. Attention is paid to iterative methods for simultaneous determination of polynomial zeros in the spirit of Smale...

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Principais autores: Petković, Miodrag., SpringerLink (Online service)
Formato: Digital
Publicado em:
Assuntos:
Matemática.
Análise numérica.
Endereço do item:http://dx.doi.org/10.1007/978-3-540-77851-6
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spelling oai:localhost:123456789-2121202023-07-17T15:13:14Z Point Estimation of Root Finding Methods Petković, Miodrag. SpringerLink (Online service) Matemática. Análise numérica. This book sets out to state computationally verifiable initial conditions for predicting the immediate appearance of the guaranteed and fast convergence of iterative root finding methods. Attention is paid to iterative methods for simultaneous determination of polynomial zeros in the spirit of Smale's point estimation theory, introduced in 1986. Some basic concepts and Smale's theory for Newton's method, together with its modifications and higher-order methods, are presented in the first two chapters. The remaining chapters contain the recent author's results on initial conditions guaranteing convergence of a wide class of iterative methods for solving algebraic equations. These conditions are of practical interest since they depend only on available data, the information of a function whose zeros are sought and initial approximations. The convergence approach presented can be applied in designing a package for the simultaneous approximation of polynomial zeros. 0 2022-10-11T17:32:59Z 2022-10-11T17:32:59Z 2008. Digital 51 P752 9783540778516 197834 http://dx.doi.org/10.1007/978-3-540-77851-6 http://dx.doi.org/10.1007/978-3-540-77851-6
institution Acervo SISBI
collection SIGAA
topic Matemática.
Análise numérica.
spellingShingle Matemática.
Análise numérica.
Petković, Miodrag.
SpringerLink (Online service)
Point Estimation of Root Finding Methods
description This book sets out to state computationally verifiable initial conditions for predicting the immediate appearance of the guaranteed and fast convergence of iterative root finding methods. Attention is paid to iterative methods for simultaneous determination of polynomial zeros in the spirit of Smale's point estimation theory, introduced in 1986. Some basic concepts and Smale's theory for Newton's method, together with its modifications and higher-order methods, are presented in the first two chapters. The remaining chapters contain the recent author's results on initial conditions guaranteing convergence of a wide class of iterative methods for solving algebraic equations. These conditions are of practical interest since they depend only on available data, the information of a function whose zeros are sought and initial approximations. The convergence approach presented can be applied in designing a package for the simultaneous approximation of polynomial zeros.
format Digital
author Petković, Miodrag.
SpringerLink (Online service)
author_facet Petković, Miodrag.
SpringerLink (Online service)
author_sort Petković, Miodrag.
title Point Estimation of Root Finding Methods
title_short Point Estimation of Root Finding Methods
title_full Point Estimation of Root Finding Methods
title_fullStr Point Estimation of Root Finding Methods
title_full_unstemmed Point Estimation of Root Finding Methods
title_sort point estimation of root finding methods
publishDate 2022
url http://dx.doi.org/10.1007/978-3-540-77851-6
work_keys_str_mv AT petkovi263miodrag pointestimationofrootfindingmethods
AT springerlinkonlineservice pointestimationofrootfindingmethods
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