TY - JOUR

T1 - Rational and radical fixed point functions for the eigenvalue problem and polynomials

AU - Hasan, Jawad A.K.

AU - Hasan, Mohammed A.

PY - 2001/1/1

Y1 - 2001/1/1

N2 - 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.

AB - 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.

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U2 - 10.1109/ICASSP.2001.941106

DO - 10.1109/ICASSP.2001.941106

M3 - Article

AN - SCOPUS:0034846581

VL - 2

SP - 1077

EP - 1080

JO - Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing

JF - Proceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing

SN - 0736-7791

ER -