An Urabe Type A Posteriori Stopping Criterion and a Globally Convergent Property of the Simplicial Approximate Homotopy Method

Mitsunori MAKINO; Shin'ichi OISHI; Masahide KASHIWAGI; Kazuo HORIUCHI

An Urabe Type A Posteriori Stopping Criterion and a Globally Convergent Property of the Simplicial Approximate Homotopy Method

Mitsunori MAKINO, Shin'ichi OISHI, Masahide KASHIWAGI, Kazuo HORIUCHI

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In this paper, in the first place, a slightly version upped Urabe type theorem of convergence criterion is presented for the modified Newton method. Then, based on this theorem, a posteriori stopping criterion is presented for a class of numerical methods of calculating solutions including the simplicial approximate homotopy method for nonlinear equations. By this criterion it is estimated whether an approximate solution satisfies the conditions of the Urabe theorem or not. Finally, it is shown that under a certain mild condition a class of simplicial approximate homotopy methods such as Merrill's method generate an approximate solution which satisfies our stopping criterion in restarting finite steps.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E74-A No.6 pp.1440-1446

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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Mitsunori MAKINO
Shin'ichi OISHI
Masahide KASHIWAGI
Kazuo HORIUCHI

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Mitsunori MAKINO, Shin'ichi OISHI, Masahide KASHIWAGI, Kazuo HORIUCHI, "An Urabe Type A Posteriori Stopping Criterion and a Globally Convergent Property of the Simplicial Approximate Homotopy Method" in IEICE TRANSACTIONS on Fundamentals, vol. E74-A, no. 6, pp. 1440-1446, June 1991, doi: .
Abstract: In this paper, in the first place, a slightly version upped Urabe type theorem of convergence criterion is presented for the modified Newton method. Then, based on this theorem, a posteriori stopping criterion is presented for a class of numerical methods of calculating solutions including the simplicial approximate homotopy method for nonlinear equations. By this criterion it is estimated whether an approximate solution satisfies the conditions of the Urabe theorem or not. Finally, it is shown that under a certain mild condition a class of simplicial approximate homotopy methods such as Merrill's method generate an approximate solution which satisfies our stopping criterion in restarting finite steps.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e74-a_6_1440/_p

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@ARTICLE{e74-a_6_1440,
author={Mitsunori MAKINO, Shin'ichi OISHI, Masahide KASHIWAGI, Kazuo HORIUCHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={An Urabe Type A Posteriori Stopping Criterion and a Globally Convergent Property of the Simplicial Approximate Homotopy Method},
year={1991},
volume={E74-A},
number={6},
pages={1440-1446},
abstract={In this paper, in the first place, a slightly version upped Urabe type theorem of convergence criterion is presented for the modified Newton method. Then, based on this theorem, a posteriori stopping criterion is presented for a class of numerical methods of calculating solutions including the simplicial approximate homotopy method for nonlinear equations. By this criterion it is estimated whether an approximate solution satisfies the conditions of the Urabe theorem or not. Finally, it is shown that under a certain mild condition a class of simplicial approximate homotopy methods such as Merrill's method generate an approximate solution which satisfies our stopping criterion in restarting finite steps.},
keywords={},
doi={},
ISSN={},
month={June},}

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TY - JOUR
TI - An Urabe Type A Posteriori Stopping Criterion and a Globally Convergent Property of the Simplicial Approximate Homotopy Method
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1440
EP - 1446
AU - Mitsunori MAKINO
AU - Shin'ichi OISHI
AU - Masahide KASHIWAGI
AU - Kazuo HORIUCHI
PY - 1991
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E74-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 1991
AB - In this paper, in the first place, a slightly version upped Urabe type theorem of convergence criterion is presented for the modified Newton method. Then, based on this theorem, a posteriori stopping criterion is presented for a class of numerical methods of calculating solutions including the simplicial approximate homotopy method for nonlinear equations. By this criterion it is estimated whether an approximate solution satisfies the conditions of the Urabe theorem or not. Finally, it is shown that under a certain mild condition a class of simplicial approximate homotopy methods such as Merrill's method generate an approximate solution which satisfies our stopping criterion in restarting finite steps.
ER -