Abstract
A matrix expression for solving large sets linear equation obtained from differential approximation of ellyptic differential equation is characterized by having less number of matrix elements, symmetry, and linear constant values. The solution of this equation does not exist singly, but often depends upon characteristics of the coefficient matrix. Therefore, determining which solution is the best is very important. This paper takes up the incomplete approximate factorization procedures conjugate gradient method and Chebyshev semi-iterative method as the three iterative calculation methods characterized in that the basic conceptions to the solution differ with each other. The paper describes the basic conceptions to the solution, geometrical considerations, improvements in the calculation efficiency and method for constructing coefficient matrices. Numerical calculations were carried out based on the convergent rate, the error analysis, and the improved method, and the result was compared with the convergent rate for further discussion. 19 refs., 14 figs.
Nishimura, H
[1]
- National Aerospace Laboratory, Tokyo (Japan)
Citation Formats
Nishimura, H.
Improvements for obtaining iterative solutions of large linear systems; Tagen renritsu ichiji hoteishiki ni taisuru hanpuku keisanho no kairyo ni tsuite.
Japan: N. p.,
1992.
Web.
Nishimura, H.
Improvements for obtaining iterative solutions of large linear systems; Tagen renritsu ichiji hoteishiki ni taisuru hanpuku keisanho no kairyo ni tsuite.
Japan.
Nishimura, H.
1992.
"Improvements for obtaining iterative solutions of large linear systems; Tagen renritsu ichiji hoteishiki ni taisuru hanpuku keisanho no kairyo ni tsuite."
Japan.
@misc{etde_10125817,
title = {Improvements for obtaining iterative solutions of large linear systems; Tagen renritsu ichiji hoteishiki ni taisuru hanpuku keisanho no kairyo ni tsuite}
author = {Nishimura, H}
abstractNote = {A matrix expression for solving large sets linear equation obtained from differential approximation of ellyptic differential equation is characterized by having less number of matrix elements, symmetry, and linear constant values. The solution of this equation does not exist singly, but often depends upon characteristics of the coefficient matrix. Therefore, determining which solution is the best is very important. This paper takes up the incomplete approximate factorization procedures conjugate gradient method and Chebyshev semi-iterative method as the three iterative calculation methods characterized in that the basic conceptions to the solution differ with each other. The paper describes the basic conceptions to the solution, geometrical considerations, improvements in the calculation efficiency and method for constructing coefficient matrices. Numerical calculations were carried out based on the convergent rate, the error analysis, and the improved method, and the result was compared with the convergent rate for further discussion. 19 refs., 14 figs.}
place = {Japan}
year = {1992}
month = {Feb}
}
title = {Improvements for obtaining iterative solutions of large linear systems; Tagen renritsu ichiji hoteishiki ni taisuru hanpuku keisanho no kairyo ni tsuite}
author = {Nishimura, H}
abstractNote = {A matrix expression for solving large sets linear equation obtained from differential approximation of ellyptic differential equation is characterized by having less number of matrix elements, symmetry, and linear constant values. The solution of this equation does not exist singly, but often depends upon characteristics of the coefficient matrix. Therefore, determining which solution is the best is very important. This paper takes up the incomplete approximate factorization procedures conjugate gradient method and Chebyshev semi-iterative method as the three iterative calculation methods characterized in that the basic conceptions to the solution differ with each other. The paper describes the basic conceptions to the solution, geometrical considerations, improvements in the calculation efficiency and method for constructing coefficient matrices. Numerical calculations were carried out based on the convergent rate, the error analysis, and the improved method, and the result was compared with the convergent rate for further discussion. 19 refs., 14 figs.}
place = {Japan}
year = {1992}
month = {Feb}
}