Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Computer Methods for Circuit Analysis and Design
Computer Methods for Circuit Analysis and Design
ApaTools: a software toolbox for approximate polynomial algebra
ACM Communications in Computer Algebra
New methods for improving the pole-zero analysis accuracy
MMES'10 Proceedings of the 2010 international conference on Mathematical models for engineering science
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The paper deals with a method for accurate computation of multiple poles and zeros in semisymbolic analysis of idealized linear circuits. The well known problem of the QR and QZ algorithms is their poor accuracy in case of multiple roots, which is usually compensated by the use of slow multiprecision arithmetic. The method presented in this paper is based on an improved reduction procedure for transforming generalized eigenproblem into the standard one in combination with an algorithm for computing the Jordan canonical form of inexact matrices [1]. The reduction procedure uses the SVD method for explicit rank estimation with the aim of avoiding the reporting of spurious roots. Numerical experiments have shown the numerical accuracy to be maintained even for defect matrices with high multiplicity roots.