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Fast Algorithms for Solving Toeplitz and Bordered Toeplitz Matrix Equations Arising in Electromagnetic Theory
MinHua HO Mingchih CHEN
Publication
IEICE TRANSACTIONS on Electronics
Vol.E88C
No.6
pp.12951303 Publication Date: 2005/06/01 Online ISSN:
DOI: 10.1093/ietele/e88c.6.1295 Print ISSN: 09168516 Type of Manuscript: PAPER Category: Electromagnetic Theory Keyword: Toeplitz matrix, bordered Toeplitz matrix, recursive algorithm, moment method, Galerkin's method,
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Summary:
In many electromagnetic field problems, matrix equations were always deduced from using the method of moment. Among these matrix equations, some of them might require a large amount of computer memory storage which made them unrealistic to be solved on a personal computer. Virtually, these matrices might be too large to be solved efficiently. A fast algorithm based on a Toeplitz matrix solution was developed for solving a bordered Toeplitz matrix equation arising in electromagnetic problems applications. The developed matrix solution method can be applied to solve some electromagnetic problems having very largescale matrices, which are deduced from the moment method procedure. In this paper, a study of a computationally efficient orderrecursive algorithm for solving the linear electromagnetic problems [Z]I = V, where [Z] is a Toeplitz matrix, was presented. Upon the described Toeplitz matrix algorithm, this paper derives an efficient recursive algorithm for solving a bordered Toeplitz matrix with the matrix's major portion in the form of a Toeplitz matrix. This algorithm has remarkable advantages in reducing both the number of arithmetic operations and memory storage.

