New higher-order methods for the simultaneous inclusion of polynomial zeros

DOI10.1007/s11075-011-9452-yzbMath1231.65083OpenAlexW1984230032MaRDI QIDQ639989

Mimica R. Milošević, Miodrag S. Petković, Dušan M. Milošević

Publication date: 11 October 2011

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-011-9452-y

zbMATH Keywords

convergencenumerical exampleshigh-order methodspolynomial zeroscomplex zerossimultaneous methodsinclusion methodsmultiple zerosGargantini-Henrici's inclusion methodGauss-Seidel approach

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 roots of polynomial equations (65H04)

Uses Software

• gmp
• MPFR

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new fourth-order iterative method for finding multiple roots of nonlinear equations
• Numerical methods for roots of polynomials. Part I
• The self-validated method for polynomial zeros of high efficiency
• On a generalisation of the root iterations for polynomial complex zeros in circular interval arithmetic
• A modification of Newton's method for analytic mappings having multiple zeros
• An improvement of Gargantini's simultaneous inclusion method for polynomial roots by Schröder's correction
• Weierstrass formula and zero-finding methods
• A method for finding the zeros of polynomials using a companion matrix.
• Iterative methods for simultaneous inclusion of polynomial zeros
• Some improved inclusion methods for polynomial roots with Weierstrass' corrections
• Fast multiplication of large numbers
• Circular arithmetic and the determination of polynomial zeros
• Improved Halley-like methods for the inclusion of polynomial zeros
• Modern Computer Arithmetic
• On a new family of simultaneous methods with corrections for the inclusion of polynomial zeros
• MPFR
• An Existence Test for Root Clusters and Multiple Roots
• On Halley-Like Algorithms for Simultaneous Approximation of Polynomial Complex Zeros
• Further Applications of Circular Arithmetic: Schroeder-Like Algorithms with Error Bounds for Finding Zeros of Polynomials
• Some Efficient Algorithms for Solving Systems of Nonlinear Equations

This page was built for publication: New higher-order methods for the simultaneous inclusion of polynomial zeros