A high-order iterative formula for simultaneous determination of zeros of a polynomial

DOI10.1016/0377-0427(91)90184-LzbMath0753.65042MaRDI QIDQ1184136

Tatsuo Torii, Tetsuya Sakurai, Sugiura, Hiroshi

Publication date: 28 June 1992

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

zbMATH Keywords

algorithmsnumerical resultsPadé approximationmultiple rootshigh convergence orderroot finding algorithmhigh-order iterative formulasingle-root methodzeros of a complex polynomial

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) Numerical computation of solutions to single equations (65H05)

Related Items (16)

ON HIGHLY EFFICIENT SIMULTANEOUS SCHEMES FOR FINDING ALL POLYNOMIAL ROOTS ⋮ Family of simultaneous methods of Hansen--Patrick's type ⋮ A note on determinantal representation of a Schröder-König-like simultaneous method for finding polynomial zeros ⋮ Simultaneous factorization of a polynomial by rational approximation ⋮ Jacobi-free and complex-free method for finding simultaneously all zeros of polynomials having only real zeros ⋮ Construction of zero-finding methods by Weierstrass functions ⋮ On some simultaneous methods based on Weierstrass' correction ⋮ A family of simultaneous zero-finding methods ⋮ A new family of Sakurai-Torii-Sugiura type iterative methods with high order of convergence ⋮ Convergence analysis of Sakurai-Torii-Sugiura iterative method for simultaneous approximation of polynomial zeros ⋮ A class of simultaneous methods for the zeros of analytic functions ⋮ On new higher order families of simultaneous methods for finding polynomial zeros ⋮ Numerical factorization of a polynomial by rational Hermite interpolation ⋮ An efficient higher order family of root finders ⋮ The convergence of a family of parallel zero-finding methods ⋮ Computer methodologies for comparison of computational efficiency of simultaneous methods for finding polynomial zeros

Cites Work

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• Padé-type approximation and general orthogonal polynomials
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• Generalised Root Iterations for the Simultaneous Determination of Multiple Complex Zeros
• A class of Iteration functions for improving, simultaneously, approximations to the zeros of a polynomial
• Iteration Methods for Finding all Zeros of a Polynomial Simultaneously

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