A Contribution to the Numerics of Polynomials and Matrix Polynomials
Sigurd Falk
TL;DR
This paper introduces algorithms for calculating zeros of polynomials and eigenvalues of polynomial matrices with multiplicities greater than one, using MATLAB for initial values and demonstrating reliability through multiple examples.
Contribution
The paper presents new algorithms specifically designed for polynomials and matrix polynomials with multiple roots, enhancing numerical stability and accuracy.
Findings
Algorithms successfully compute zeros and eigenvalues with high reliability.
Numerical experiments confirm the effectiveness of the proposed methods.
MATLAB initial values improve convergence and accuracy.
Abstract
In this paper some algorithms will be presented which can be used for the calculation of zeros of polynomials and eigenvalues of polynomial matrices with a multiplicity larger than one. The numerical values calculated with MATLAB are used as starting values. The reliability of the algorithms is demonstrated by means of 8 examples.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Mathematical Theories and Applications