A Path Following Algorithm for Finding All the Solutions on Non-linear Equation System in a Compact Region

Hisato FUJISAKA; Hisakazu NISHINO; Chikara SATO; Yuuji SATOH

IEICE TRANSACTIONS on Fundamentals

A Path Following Algorithm for Finding All the Solutions on Non-linear Equation System in a Compact Region

Hisato FUJISAKA, Hisakazu NISHINO, Chikara SATO, Yuuji SATOH

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We propose a method to search all the zeros of a complex function in a given compact region D Cⁿ. The function f: Cⁿ Cⁿ to be considered is assumed to consist of polynomial and transcendental terms and to satisfy f (x) Rⁿ for any x Rⁿ. Using the properties of such a complex function, we can compute the number of zeros and determine the starting points of paths on the boundary of D, which attain all the zeros of f in D without encountering a singular point. A piecewiselinear approximation of the function on a triangulation is used for both computing the number of zeros and following the paths.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E80-A No.11 pp.2308-2317

Publication Date: 1997/11/25

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Category: Numerical Analysis and Optimization

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Hisato FUJISAKA, Hisakazu NISHINO, Chikara SATO, Yuuji SATOH, "A Path Following Algorithm for Finding All the Solutions on Non-linear Equation System in a Compact Region" in IEICE TRANSACTIONS on Fundamentals, vol. E80-A, no. 11, pp. 2308-2317, November 1997, doi: .
Abstract: We propose a method to search all the zeros of a complex function in a given compact region D Cⁿ. The function f: Cⁿ Cⁿ to be considered is assumed to consist of polynomial and transcendental terms and to satisfy f (x) Rⁿ for any x Rⁿ. Using the properties of such a complex function, we can compute the number of zeros and determine the starting points of paths on the boundary of D, which attain all the zeros of f in D without encountering a singular point. A piecewiselinear approximation of the function on a triangulation is used for both computing the number of zeros and following the paths.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e80-a_11_2308/_p

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@ARTICLE{e80-a_11_2308,
author={Hisato FUJISAKA, Hisakazu NISHINO, Chikara SATO, Yuuji SATOH, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Path Following Algorithm for Finding All the Solutions on Non-linear Equation System in a Compact Region},
year={1997},
volume={E80-A},
number={11},
pages={2308-2317},
abstract={We propose a method to search all the zeros of a complex function in a given compact region D Cⁿ. The function f: Cⁿ Cⁿ to be considered is assumed to consist of polynomial and transcendental terms and to satisfy f (x) Rⁿ for any x Rⁿ. Using the properties of such a complex function, we can compute the number of zeros and determine the starting points of paths on the boundary of D, which attain all the zeros of f in D without encountering a singular point. A piecewiselinear approximation of the function on a triangulation is used for both computing the number of zeros and following the paths.},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - A Path Following Algorithm for Finding All the Solutions on Non-linear Equation System in a Compact Region
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2308
EP - 2317
AU - Hisato FUJISAKA
AU - Hisakazu NISHINO
AU - Chikara SATO
AU - Yuuji SATOH
PY - 1997
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E80-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 1997
AB - We propose a method to search all the zeros of a complex function in a given compact region D Cⁿ. The function f: Cⁿ Cⁿ to be considered is assumed to consist of polynomial and transcendental terms and to satisfy f (x) Rⁿ for any x Rⁿ. Using the properties of such a complex function, we can compute the number of zeros and determine the starting points of paths on the boundary of D, which attain all the zeros of f in D without encountering a singular point. A piecewiselinear approximation of the function on a triangulation is used for both computing the number of zeros and following the paths.
ER -

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A Path Following Algorithm for Finding All the Solutions on Non-linear Equation System in a Compact Region

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A Path Following Algorithm for Finding All the Solutions on Non-linear Equation System in a Compact Region

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