Rational and radical fixed point functions for the eigenvalue problem and polynomials

Jawad A.K. Hasan, Mohammed A. Hasan

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

The derivation and implementation of many algorithms in signal/image processing and control involve some form of polynomial root-finding and/or matrix eigendecomposition. In this paper, higher order fixed point functions in rational and/or radical forms are developed. This set of iterations can be considered as extensions of known methods such as Newton's, Laguerre's and Halley's methods and can be applied to compute all zeros of a polynomial as well as all eigenvalues of a complex matrix. One of the main features of the proposed algorithms is that they could have any predetermined rate of convergence regardless of the multiplicity of the zeros or eigenvalues. Additionally, eigenvalues and eigenvectors are computed using fast matrix inverse free algorithms which are based on the QR factorization.

Original languageEnglish (US)
Pages (from-to)1077-1080
Number of pages4
JournalICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2
DOIs
StatePublished - Jan 1 2001

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