Generalizations of Laguerre’s Method: Higher Order Methods

DOI10.1137/0718069zbMath0554.65036OpenAlexW2014326812MaRDI QIDQ3217524

Leslie V. Foster

Publication date: 1981

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0718069

zbMATH Keywords

numerical resultszeros of polynomialseigenvalue problemsorder of convergencegeneralized Hermite interpolationLaguerre's methodhyperosculatory interpolation

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Numerical computation of solutions to single equations (65H05)

Related Items (11)

On optimal parameter of Laguerre's family of zero-finding methods ⋮ On the dynamics of Laguerre's iteration: \(Z^ n-1\) ⋮ Repellers for the Laguerre Iteration Function ⋮ The computation of multiple roots of a polynomial ⋮ The quasi-Laguerre iteration ⋮ Several new methods for solving equations ⋮ Approximating complex polynomial zeros: modified Weyl's quadtree construction and improved Newton's iteration. ⋮ Structured matrix methods for the computation of multiple roots of a polynomial ⋮ Choosing improved initial values for polynomial zerofinding in extended Newbery method to obtain convergence ⋮ On the global convergence of Schröder's iterative formulae for real roots of algebraic equations ⋮ An effective implementation of a modified Laguerre method for the roots of a polynomial

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