Higher order convergent algorithms with applications to polynomials and matrices

Mohammed A. Hasan

Higher order convergent algorithms with applications to polynomials and matrices

Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

New stable higher order algorithms for computing matrix nth root are presented. Specifically, a generalization of Denman-Beaver iteration for matrix square and cubic roots are given. The new iterations are obtained by change of variables applied to variations of Newton's method and higher order methods. Extensions of these methods for orthonormalization of a rectangular matrix with respect to a positive definite matrix are also given.

Original language	English (US)
Title of host publication	ISCAS 2006
Subtitle of host publication	2006 IEEE International Symposium on Circuits and Systems, Proceedings
Pages	3698-3701
Number of pages	4
State	Published - Dec 1 2006
Event	ISCAS 2006: 2006 IEEE International Symposium on Circuits and Systems - Kos, Greece Duration: May 21 2006 → May 24 2006

Publication series

Name	Proceedings - IEEE International Symposium on Circuits and Systems
ISSN (Print)	0271-4310

Other

Other	ISCAS 2006: 2006 IEEE International Symposium on Circuits and Systems
Country/Territory	Greece
City	Kos
Period	5/21/06 → 5/24/06

Keywords

Denman-beaver iteration
Matrix nth root
Matrix sign function
Newton's method
Orthonormalization

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Higher order convergent algorithms with applications to polynomials and matrices. / Hasan, Mohammed A.
ISCAS 2006: 2006 IEEE International Symposium on Circuits and Systems, Proceedings. 2006. p. 3698-3701 1693430 (Proceedings - IEEE International Symposium on Circuits and Systems).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Hasan, MA 2006, Higher order convergent algorithms with applications to polynomials and matrices. in ISCAS 2006: 2006 IEEE International Symposium on Circuits and Systems, Proceedings., 1693430, Proceedings - IEEE International Symposium on Circuits and Systems, pp. 3698-3701, ISCAS 2006: 2006 IEEE International Symposium on Circuits and Systems, Kos, Greece, 5/21/06.

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AB - New stable higher order algorithms for computing matrix nth root are presented. Specifically, a generalization of Denman-Beaver iteration for matrix square and cubic roots are given. The new iterations are obtained by change of variables applied to variations of Newton's method and higher order methods. Extensions of these methods for orthonormalization of a rectangular matrix with respect to a positive definite matrix are also given.

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KW - Matrix sign function

KW - Newton's method

KW - Orthonormalization

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BT - ISCAS 2006

T2 - ISCAS 2006: 2006 IEEE International Symposium on Circuits and Systems

Y2 - 21 May 2006 through 24 May 2006

ER -

Higher order convergent algorithms with applications to polynomials and matrices

Abstract

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