Characterization of the determinant of a Laguerre matrix

DOI10.1007/s12190-010-0399-2zbMath1221.15041OpenAlexW1979961086MaRDI QIDQ545584

Vu Quoc Phong, Sang-Gu Lee, YoonMee Ham

Publication date: 22 June 2011

Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12190-010-0399-2

zbMATH Keywords

Newton's methodToeplitz matrixLaguerre's iteration functionzeros of an analytic function

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Numerical computation of solutions to single equations (65H05) Toeplitz, Cauchy, and related matrices (15B05)

Cites Work

• Are there any Julia sets for the Laguerre iteration function?
• Selection of good algorithms from a family of algorithms for polynomial derivative evaluation
• A basic family of iteration functions for polynomial root finding and its characterizations
• Newton's method and generation of a determinantal family of iteration functions
• On the Laguerre Method for Separating the Roots of Algebraic Equations
• An infinite family of bounds on zeros of analytic functions and relationship to Smale’s bound

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