TY - JOUR

T1 - Fast algorithms for solving toeplitz and bordered toeplitz matrix equations arising in electromagnetic theory

AU - Ho, Min Hua

AU - Chen, Mingchih

PY - 2005/6

Y1 - 2005/6

N2 - 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 large-scale matrices, which are deduced from the moment method procedure. In this paper, a study of a computationally efficient order-recursive 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.

AB - 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 large-scale matrices, which are deduced from the moment method procedure. In this paper, a study of a computationally efficient order-recursive 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.

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U2 - 10.1093/ietele/e88-c.6.1295

DO - 10.1093/ietele/e88-c.6.1295

M3 - Article

AN - SCOPUS:25844473230

VL - E88-C

SP - 1295

EP - 1303

JO - IEICE Transactions on Electronics

JF - IEICE Transactions on Electronics

SN - 0916-8524

IS - 6

ER -