Zero-clusters of polynomials: best approach in supercomputing era

DOI10.1016/j.amc.2009.11.017zbMath1186.65059OpenAlexW1964845131MaRDI QIDQ961599

Ravi P. Agarwal, Syamal K. Sen

Publication date: 31 March 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2009.11.017

zbMATH Keywords

numerical examplesmultiple rootsrandomized methodsexhaustive search algorithmcomputational errorsupercomputing eracomputational/time complexitydeflated Newton methodreal/complex zero-clusterzero-clusters of polynomials

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) Real polynomials: location of zeros (26C10) Numerical computation of roots of polynomial equations (65H04)

Uses Software

• BRENT

Cites Work

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• Computational error and complexity in science and engineering
• Best \(k\)-digit rational bounds for irrational numbers: pre- and super-computer era
• The evaluation of polynomials
• The Cyclic Jacobi Method for Computing the Principal Values of a Complex Matrix
• The QR Transformation A Unitary Analogue to the LR Transformation--Part 1
• Instability of the Elimination Method of Reducing a Matrix to Tri-diagonal Form

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