Application of the conjugate gradient and steepest descent for computing the eigenvalues of an operator

Tapan K. Sarkar; Xiaopu Yang

doi:10.1016/0165-1684(89)90070-4

Application of the conjugate gradient and steepest descent for computing the eigenvalues of an operator

Tapan K. Sarkar, Xiaopu Yang

Department of Electrical Engineering & Computer Science

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

This paper describes the method of steepest descent and the method of conjugate gradient for iteratively finding the first few large/small eigenvalues and eigenvectors of a Hermitian operator. Both the methods have been applied for the computation of the prolate spheroidal functions. Since the methods are iterative, it is expected to yield accurate solutions for the first few large/small eigenvalues particularly when the condition number (ratio of the largest to the smallest eigenvalue) is large.

Original language	English (US)
Pages (from-to)	31-38
Number of pages	8
Journal	Signal Processing
Volume	17
Issue number	1
DOIs	https://doi.org/10.1016/0165-1684(89)90070-4
State	Published - May 1989

Keywords

Hermetian operators
conjugate gradient
steepest descent

ASJC Scopus subject areas

Control and Systems Engineering
Software
Signal Processing
Computer Vision and Pattern Recognition
Electrical and Electronic Engineering

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10.1016/0165-1684(89)90070-4

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AB - This paper describes the method of steepest descent and the method of conjugate gradient for iteratively finding the first few large/small eigenvalues and eigenvectors of a Hermitian operator. Both the methods have been applied for the computation of the prolate spheroidal functions. Since the methods are iterative, it is expected to yield accurate solutions for the first few large/small eigenvalues particularly when the condition number (ratio of the largest to the smallest eigenvalue) is large.

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Application of the conjugate gradient and steepest descent for computing the eigenvalues of an operator

Abstract

Keywords

ASJC Scopus subject areas

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