ENGLISH

Point Estimation of Root Finding Methods

By Miodrag Petković (eds.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2008
ISBN
3540778500, 9783540778509
DOI
10.1007/978-3-540-77851-6
Open Library ID
OL21897320M
Language
english
Format
PDF
Filesize
2 MB (1896580 bytes)
Series
Lecture Notes in Mathematics 1933
Edition
1
Pages
210\223
Orientation
no
Scanned
no
Time added
2011-04-28 18:43:47
Numerical Analysis

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.

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