Fast Algorithms for Solving Toeplitz and Bordered Toeplitz Matrix Equations Arising in Electromagnetic Theory

Min-Hua HO; Mingchih CHEN

doi:10.1093/ietele/e88-c.6.1295

Fast Algorithms for Solving Toeplitz and Bordered Toeplitz Matrix Equations Arising in Electromagnetic Theory

Min-Hua HO, Mingchih CHEN

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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.

Publication: IEICE TRANSACTIONS on Electronics Vol.E88-C No.6 pp.1295-1303

Publication Date: 2005/06/01

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DOI: 10.1093/ietele/e88-c.6.1295

Type of Manuscript: PAPER

Category: Electromagnetic Theory

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Min-Hua HO, Mingchih CHEN, "Fast Algorithms for Solving Toeplitz and Bordered Toeplitz Matrix Equations Arising in Electromagnetic Theory" in IEICE TRANSACTIONS on Electronics, vol. E88-C, no. 6, pp. 1295-1303, June 2005, doi: 10.1093/ietele/e88-c.6.1295.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/electronics/10.1093/ietele/e88-c.6.1295/_p

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@ARTICLE{e88-c_6_1295,
author={Min-Hua HO, Mingchih CHEN, },
journal={IEICE TRANSACTIONS on Electronics},
title={Fast Algorithms for Solving Toeplitz and Bordered Toeplitz Matrix Equations Arising in Electromagnetic Theory},
year={2005},
volume={E88-C},
number={6},
pages={1295-1303},
abstract={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.},
keywords={},
doi={10.1093/ietele/e88-c.6.1295},
ISSN={},
month={June},}

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TY - JOUR
TI - Fast Algorithms for Solving Toeplitz and Bordered Toeplitz Matrix Equations Arising in Electromagnetic Theory
T2 - IEICE TRANSACTIONS on Electronics
SP - 1295
EP - 1303
AU - Min-Hua HO
AU - Mingchih CHEN
PY - 2005
DO - 10.1093/ietele/e88-c.6.1295
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E88-C
IS - 6
JA - IEICE TRANSACTIONS on Electronics
Y1 - June 2005
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.
ER -