Point estimation of root finding methods / Miodrag Petković
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1933Langue : anglais.Éditeur : Berlin : Springer, 2008ISBN: 9783540778509.ISSN: 1617-9692.Sujet MSC : 65H05, Numerical analysis - Nonlinear algebraic or transcendental equations, Numerical computation of solutions to single equations12-08, Computational methods for problems pertaining to field theory
26C10, Real functions - Polynomials, rational functions in real analysis, Real polynomials: location of zeros
30C15, Functions of a complex variable - Geometric function theory, Zeros of polynomials, rational functions, and other analytic functions of one complex variableEn-ligne : Springerlink | Zentralblatt | MathSciNet
n this book, the author presents the basic concepts for convergent root finding methods and studies estimations of zero finding methods from data at one point using Smale’s point estimation theory, by constructing such initial conditions, providing guaranteed convergence. Furthermore the author proposes the construction of computationally verifiable initial conditions and studies the corresponding convergence analysis of the simultaneous methods, which predict the immediate appearance of the guaranteed and fast convergence of iterative root finding methods. Additionally, the author presents higher order families of simultaneous methods for the determination of polynomial (simple or multiple) zeros. Finally, numerical results, illustrating the convergence behavior, are presented. (Zentralblatt)
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