IEICE TRANSACTIONS on transactions
Computational Complexity of Calculating Solutions for a Certain Class of Uniquely Solvable Nonlinear Equation by Homotopy Method
Summary :
A priori estimation is presented for a computational complexity of the homotopy method applying to a certain class of uniquely solvable nonlinear equations. In the first place, the reason is explained why a computational complexity of the homotopy method can not be a priori estimated in general. In this paper, the homotopy algorithm is considered in which a numerical path following algorithm is executed based on the simplified Newton method. Then by introducing Urabe's theorem, which gives a sufficient condition guaranteeing the convergence of the simplified Newton method, it is shown that a computational complexity of the algorithm can be a priori estimated, when it is applied to a certain class of uniquely solvable nonlinear equation. In this paper, two types of path following algorithms are considered, one with a numerical error estimation in the domain of a nonlinear operator and another with one in the range of the operator.
- Publication
- IEICE TRANSACTIONS on transactions Vol.E73-E No.12 pp.1940-1947
- Publication Date
- 1990/12/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- Special Section PAPER (Special Issue on the 3rd Karuizawa Workshop on Circuits and Systems)
- Category
- Nonlinear Circuits and Simulation
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Mitsunori MAKINO, Shin'ichi OISHI, Masahide KASHIWAGI, Kazuo HORIUCHI, "Computational Complexity of Calculating Solutions for a Certain Class of Uniquely Solvable Nonlinear Equation by Homotopy Method" in IEICE TRANSACTIONS on transactions,
vol. E73-E, no. 12, pp. 1940-1947, December 1990, doi: .
Abstract: A priori estimation is presented for a computational complexity of the homotopy method applying to a certain class of uniquely solvable nonlinear equations. In the first place, the reason is explained why a computational complexity of the homotopy method can not be a priori estimated in general. In this paper, the homotopy algorithm is considered in which a numerical path following algorithm is executed based on the simplified Newton method. Then by introducing Urabe's theorem, which gives a sufficient condition guaranteeing the convergence of the simplified Newton method, it is shown that a computational complexity of the algorithm can be a priori estimated, when it is applied to a certain class of uniquely solvable nonlinear equation. In this paper, two types of path following algorithms are considered, one with a numerical error estimation in the domain of a nonlinear operator and another with one in the range of the operator.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e73-e_12_1940/_p
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@ARTICLE{e73-e_12_1940,
author={Mitsunori MAKINO, Shin'ichi OISHI, Masahide KASHIWAGI, Kazuo HORIUCHI, },
journal={IEICE TRANSACTIONS on transactions},
title={Computational Complexity of Calculating Solutions for a Certain Class of Uniquely Solvable Nonlinear Equation by Homotopy Method},
year={1990},
volume={E73-E},
number={12},
pages={1940-1947},
abstract={A priori estimation is presented for a computational complexity of the homotopy method applying to a certain class of uniquely solvable nonlinear equations. In the first place, the reason is explained why a computational complexity of the homotopy method can not be a priori estimated in general. In this paper, the homotopy algorithm is considered in which a numerical path following algorithm is executed based on the simplified Newton method. Then by introducing Urabe's theorem, which gives a sufficient condition guaranteeing the convergence of the simplified Newton method, it is shown that a computational complexity of the algorithm can be a priori estimated, when it is applied to a certain class of uniquely solvable nonlinear equation. In this paper, two types of path following algorithms are considered, one with a numerical error estimation in the domain of a nonlinear operator and another with one in the range of the operator.},
keywords={},
doi={},
ISSN={},
month={December},}
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TY - JOUR
TI - Computational Complexity of Calculating Solutions for a Certain Class of Uniquely Solvable Nonlinear Equation by Homotopy Method
T2 - IEICE TRANSACTIONS on transactions
SP - 1940
EP - 1947
AU - Mitsunori MAKINO
AU - Shin'ichi OISHI
AU - Masahide KASHIWAGI
AU - Kazuo HORIUCHI
PY - 1990
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E73-E
IS - 12
JA - IEICE TRANSACTIONS on transactions
Y1 - December 1990
AB - A priori estimation is presented for a computational complexity of the homotopy method applying to a certain class of uniquely solvable nonlinear equations. In the first place, the reason is explained why a computational complexity of the homotopy method can not be a priori estimated in general. In this paper, the homotopy algorithm is considered in which a numerical path following algorithm is executed based on the simplified Newton method. Then by introducing Urabe's theorem, which gives a sufficient condition guaranteeing the convergence of the simplified Newton method, it is shown that a computational complexity of the algorithm can be a priori estimated, when it is applied to a certain class of uniquely solvable nonlinear equation. In this paper, two types of path following algorithms are considered, one with a numerical error estimation in the domain of a nonlinear operator and another with one in the range of the operator.
ER -
English
