### Abstract

A priori estimation is presented for a computational complexity of the homotopy method applying to a certain class of strongly monotone nonlinear equations. In the present paper, a condition is presented for a certain class of uniquely solvable equations, under which an upper bound of a computational complexity of the Newton type homotype method can be a priori estimated. In this paper, a condition is considered in a case of linear homotopy equations including the Newton type homotopy equations. In the first place the homotopy algorithm based on the simplified Newton method is introduced. Then by using Urabe type theorem, which gives a sufficient condition guaranteeing the convergence of the simplified Newton method, a condition is presented under which an upper bound of a computational complexity of the algorithm can be a priori estimated, when it is applied to a certain class of strongly monotone nonlinear equations. The presented condition is demonstrated by numerical experiments.

Original language | English |
---|---|

Pages (from-to) | 786-794 |

Number of pages | 9 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E76-A |

Issue number | 5 |

Publication status | Published - 1993 May |

Externally published | Yes |

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### ASJC Scopus subject areas

- Hardware and Architecture
- Information Systems
- Electrical and Electronic Engineering

### Cite this

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*,

*E76-A*(5), 786-794.

**Sufficient condition of a priori estimation for computational complexity of the homotopy method.** / Makino, Mitsunori; Kashiwagi, Masahide; Oishi, Shinichi; Horiuchi, Kazuo.

Research output: Contribution to journal › Article

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E76-A, no. 5, pp. 786-794.

}

TY - JOUR

T1 - Sufficient condition of a priori estimation for computational complexity of the homotopy method

AU - Makino, Mitsunori

AU - Kashiwagi, Masahide

AU - Oishi, Shinichi

AU - Horiuchi, Kazuo

PY - 1993/5

Y1 - 1993/5

N2 - A priori estimation is presented for a computational complexity of the homotopy method applying to a certain class of strongly monotone nonlinear equations. In the present paper, a condition is presented for a certain class of uniquely solvable equations, under which an upper bound of a computational complexity of the Newton type homotype method can be a priori estimated. In this paper, a condition is considered in a case of linear homotopy equations including the Newton type homotopy equations. In the first place the homotopy algorithm based on the simplified Newton method is introduced. Then by using Urabe type theorem, which gives a sufficient condition guaranteeing the convergence of the simplified Newton method, a condition is presented under which an upper bound of a computational complexity of the algorithm can be a priori estimated, when it is applied to a certain class of strongly monotone nonlinear equations. The presented condition is demonstrated by numerical experiments.

AB - A priori estimation is presented for a computational complexity of the homotopy method applying to a certain class of strongly monotone nonlinear equations. In the present paper, a condition is presented for a certain class of uniquely solvable equations, under which an upper bound of a computational complexity of the Newton type homotype method can be a priori estimated. In this paper, a condition is considered in a case of linear homotopy equations including the Newton type homotopy equations. In the first place the homotopy algorithm based on the simplified Newton method is introduced. Then by using Urabe type theorem, which gives a sufficient condition guaranteeing the convergence of the simplified Newton method, a condition is presented under which an upper bound of a computational complexity of the algorithm can be a priori estimated, when it is applied to a certain class of strongly monotone nonlinear equations. The presented condition is demonstrated by numerical experiments.

UR - http://www.scopus.com/inward/record.url?scp=0027599503&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027599503&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0027599503

VL - E76-A

SP - 786

EP - 794

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 5

ER -