Improving the Efficiency of Integer Labeling Methods for Solving Systems of Nonlinear Equations

Kiyotaka YAMAMURA; Keiko KATOU; Makoto OCHIAI

Improving the Efficiency of Integer Labeling Methods for Solving Systems of Nonlinear Equations

Kiyotaka YAMAMURA, Keiko KATOU, Makoto OCHIAI

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The integer labeling method is a simplicialtype homotopy method for solving systems of nonlinear equations with global convergence. Since this method does not require matrix operations, it is very simple and is suited to parallel computation on array processors. However, the computation time of the integer labeling method grows exponentially with the dimension n, because it uses simplicial subdivision and the number of simplices in an n-dimensional rectangle grows with n!. In this paper, we propose an efficient integer labeling method for solving systems of nonlinear equations with partially-separable mappings. Partially-separable mappings appear in various fields of science and engineering, such as nonlinear programming problems. In our method, the number of function evaluations is largely reduced by making use of the partial separability of nonlinear mappings. That is, function values of separable terms need not be evaluated as long as the labeled simplex is moving within the identical rectangle. Hence, as the number of separable terms increases, considerable improvement of the computational efficiency can be achieved.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E74-A No.6 pp.1463-1470

Publication Date: 1991/06/25

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Type of Manuscript: Special Section PAPER (Special Issue on Nonlinear Theory and Its Applications)

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Kiyotaka YAMAMURA
Keiko KATOU
Makoto OCHIAI

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Kiyotaka YAMAMURA, Keiko KATOU, Makoto OCHIAI, "Improving the Efficiency of Integer Labeling Methods for Solving Systems of Nonlinear Equations" in IEICE TRANSACTIONS on Fundamentals, vol. E74-A, no. 6, pp. 1463-1470, June 1991, doi: .
Abstract: The integer labeling method is a simplicialtype homotopy method for solving systems of nonlinear equations with global convergence. Since this method does not require matrix operations, it is very simple and is suited to parallel computation on array processors. However, the computation time of the integer labeling method grows exponentially with the dimension n, because it uses simplicial subdivision and the number of simplices in an n-dimensional rectangle grows with n!. In this paper, we propose an efficient integer labeling method for solving systems of nonlinear equations with partially-separable mappings. Partially-separable mappings appear in various fields of science and engineering, such as nonlinear programming problems. In our method, the number of function evaluations is largely reduced by making use of the partial separability of nonlinear mappings. That is, function values of separable terms need not be evaluated as long as the labeled simplex is moving within the identical rectangle. Hence, as the number of separable terms increases, considerable improvement of the computational efficiency can be achieved.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e74-a_6_1463/_p

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@ARTICLE{e74-a_6_1463,
author={Kiyotaka YAMAMURA, Keiko KATOU, Makoto OCHIAI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Improving the Efficiency of Integer Labeling Methods for Solving Systems of Nonlinear Equations},
year={1991},
volume={E74-A},
number={6},
pages={1463-1470},
abstract={The integer labeling method is a simplicialtype homotopy method for solving systems of nonlinear equations with global convergence. Since this method does not require matrix operations, it is very simple and is suited to parallel computation on array processors. However, the computation time of the integer labeling method grows exponentially with the dimension n, because it uses simplicial subdivision and the number of simplices in an n-dimensional rectangle grows with n!. In this paper, we propose an efficient integer labeling method for solving systems of nonlinear equations with partially-separable mappings. Partially-separable mappings appear in various fields of science and engineering, such as nonlinear programming problems. In our method, the number of function evaluations is largely reduced by making use of the partial separability of nonlinear mappings. That is, function values of separable terms need not be evaluated as long as the labeled simplex is moving within the identical rectangle. Hence, as the number of separable terms increases, considerable improvement of the computational efficiency can be achieved.},
keywords={},
doi={},
ISSN={},
month={June},}

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TY - JOUR
TI - Improving the Efficiency of Integer Labeling Methods for Solving Systems of Nonlinear Equations
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1463
EP - 1470
AU - Kiyotaka YAMAMURA
AU - Keiko KATOU
AU - Makoto OCHIAI
PY - 1991
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E74-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 1991
AB - The integer labeling method is a simplicialtype homotopy method for solving systems of nonlinear equations with global convergence. Since this method does not require matrix operations, it is very simple and is suited to parallel computation on array processors. However, the computation time of the integer labeling method grows exponentially with the dimension n, because it uses simplicial subdivision and the number of simplices in an n-dimensional rectangle grows with n!. In this paper, we propose an efficient integer labeling method for solving systems of nonlinear equations with partially-separable mappings. Partially-separable mappings appear in various fields of science and engineering, such as nonlinear programming problems. In our method, the number of function evaluations is largely reduced by making use of the partial separability of nonlinear mappings. That is, function values of separable terms need not be evaluated as long as the labeled simplex is moving within the identical rectangle. Hence, as the number of separable terms increases, considerable improvement of the computational efficiency can be achieved.
ER -