Error-bounds for zeroes of polynomials using complex circular arithmetic

DOI10.1007/BF02251255zbMath0629.65051OpenAlexW140619431MaRDI QIDQ1094096

Andreas Frommer, W. Straub

Publication date: 1988

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02251255

zbMATH Keywords

numerical examplescomplex circular arithmeticcomplex polynomialpolynomial zeroeserror-bounds

Mathematics Subject Classification ID

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

Cites Work

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• On a second order method for the simultaneous inclusion of polynomial complex zeros in rectangular arithmetic
• On a generalisation of the root iterations for polynomial complex zeros in circular interval arithmetic
• On an iterative method for simultaneous inclusion of polynomial complex zeros
• A posteriori error bounds for the zeros of polynomials
• Fehlerabschätzungen bei Polynomgleichungen mit dem Fixpunktsatz von Brouwer
• Residuenabschätzung für Polynom-Nullstellen mittels Lagrange-Interpolation
• Circular arithmetic and the determination of polynomial zeros
• A posteriori error bounds for the zeros of a polynomial
• Simultaneous inclusion of the zeros of a polynomial
• A remark on simultaneous inclusions of the zeros of a polynomial by Gershgorin's theorem
• Über Simultanverfahren zur Bestimmung reeller Polynomwurzeln
• Further Applications of Circular Arithmetic: Schroeder-Like Algorithms with Error Bounds for Finding Zeros of Polynomials
• Error Bounds for Zeros of a Polynomial Based Upon Gerschgorin's Theorems

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