Higher-order iterative methods for approximating zeros of analytic functions

DOI10.1016/0377-0427(92)90133-IzbMath0748.65048OpenAlexW1974318180MaRDI QIDQ1186915

Dragoslav Herceg, Miodrag S. Petković

Publication date: 28 June 1992

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

Full work available at URL: https://doi.org/10.1016/0377-0427(92)90133-i

zbMATH Keywords

convergenceanalytic functioncircular arithmeticiterative methodsinterval arithmeticfloating-point arithmeticinclusion methodsNewton correctionaccuracy controlHybrid algorithmssingle-step methods\(R\)- order of convergenceHalley correctiontotal-step methods

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Interval and finite arithmetic (65G30) 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)

Related Items (5)

Numerical integration error method for zeros of analytic functions ⋮ On a modification of the Koenig theorem ⋮ A modified Chebyshev's iterative method with at least sixth order of convergence ⋮ Tchebychef-like method for the simultaneous finding zeros of analytic functions ⋮ A class of simultaneous methods for the zeros of analytic functions

Cites Work

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• On some improvements of square root iteration for polynomial complex zeros
• On the convergence order of accelerated root iterations
• On the efficiency of some combined methods for polynomial complex zeros
• On the simultaneous determination of zeros of analytic or sectionally analytic functions
• Polynomials orthogonal on the semicircle
• On the convergence order of a modified method for simultaneous finding polynomial zeros
• Iterative methods for simultaneous inclusion of polynomial zeros
• Circular arithmetic and the determination of polynomial zeros
• A generalization of the Siewert–Burniston method for the determination of zeros of analytic functions
• 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 higher-order methods for the simultaneous approximation of multiple polynomial zeros
• On the Convergence Speed of Some Algorithms for the Simultaneous Approximation of Polynomial Roots
• Complex interval arithmetic

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