On a Class of Finite Step Iterative Methods (Conjugate Directions) for the Solution of an Operator Equation Arising in Electromagnetics

Tapan K. Sarkar, Ercument Arvas

Research output: Contribution to journalArticle

98 Scopus citations

Abstract

A class of finite step iterative methods for the solution of linear operator equations is presented. Specifically, the basic principles of the method of conjugate directions are developed. Gaussian elimination and the method of conjugate gradients are then presented as two special cases. With an arbitrary initial guess, the method of conjugate gradient always converges to the solution in at most N iterations, where N is the number of independent eigenvalues for the operator in the finite dimensional space in which the problem is being solved. The conjugate gradient method requires much less storage (~ 5N) than the conventional matrix methods (~N2) in the solution of problems of higher complexity. Also, after each iteration the quality of the solution is known in the conjugate gradient method. The conjugate gradient method is also superior to the spectral iterative method as the latter does not always converge and it doubles the complexity of a given problem, unnecessarily. Four versions of the conjugate gradient method are presented in detail, and numerical results for a thin wire scatterer are given to illustrate various properties of each version.

Original languageEnglish (US)
Pages (from-to)1058-1066
Number of pages9
JournalIEEE Transactions on Antennas and Propagation
Volume33
Issue number10
DOIs
StatePublished - Oct 1985

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Fingerprint Dive into the research topics of 'On a Class of Finite Step Iterative Methods (Conjugate Directions) for the Solution of an Operator Equation Arising in Electromagnetics'. Together they form a unique fingerprint.

  • Cite this