### Abstract

A constructive simplified Newton method is presented for calculating solutions of infinite dimensional nonlinear equations, which uses a projection scheme from an infinite dimensional space to finite dimensional subspaces. A convergence theorem of the method is shown based on Urabe's theorem. For a class of successive approximation methods containing an infinite dimensional homotopy method, a stopping criterion is shown using the convergence theorem. The authors show that under a certain condition the stopping criterion is satisfied in finite cycles of iteration.

Original language | English |
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Title of host publication | Proceedings - IEEE International Symposium on Circuits and Systems |

Publisher | Publ by IEEE |

Pages | 1236-1239 |

Number of pages | 4 |

Volume | 2 |

Publication status | Published - 1991 |

Externally published | Yes |

Event | 1991 IEEE International Symposium on Circuits and Systems Part 4 (of 5) - Singapore, Singapore Duration: 1991 Jun 11 → 1991 Jun 14 |

### Other

Other | 1991 IEEE International Symposium on Circuits and Systems Part 4 (of 5) |
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City | Singapore, Singapore |

Period | 91/6/11 → 91/6/14 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Electronic, Optical and Magnetic Materials

### Cite this

*Proceedings - IEEE International Symposium on Circuits and Systems*(Vol. 2, pp. 1236-1239). Publ by IEEE.

**An Urabe type convergence theorem for a constructive simplified Newton method in infinite dimensional spaces.** / Oishi, Shinichi; Kashiwagi, Masahide; Makino, Mitsunori; Horiuchi, Kazuo.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - IEEE International Symposium on Circuits and Systems.*vol. 2, Publ by IEEE, pp. 1236-1239, 1991 IEEE International Symposium on Circuits and Systems Part 4 (of 5), Singapore, Singapore, 91/6/11.

}

TY - GEN

T1 - An Urabe type convergence theorem for a constructive simplified Newton method in infinite dimensional spaces

AU - Oishi, Shinichi

AU - Kashiwagi, Masahide

AU - Makino, Mitsunori

AU - Horiuchi, Kazuo

PY - 1991

Y1 - 1991

N2 - A constructive simplified Newton method is presented for calculating solutions of infinite dimensional nonlinear equations, which uses a projection scheme from an infinite dimensional space to finite dimensional subspaces. A convergence theorem of the method is shown based on Urabe's theorem. For a class of successive approximation methods containing an infinite dimensional homotopy method, a stopping criterion is shown using the convergence theorem. The authors show that under a certain condition the stopping criterion is satisfied in finite cycles of iteration.

AB - A constructive simplified Newton method is presented for calculating solutions of infinite dimensional nonlinear equations, which uses a projection scheme from an infinite dimensional space to finite dimensional subspaces. A convergence theorem of the method is shown based on Urabe's theorem. For a class of successive approximation methods containing an infinite dimensional homotopy method, a stopping criterion is shown using the convergence theorem. The authors show that under a certain condition the stopping criterion is satisfied in finite cycles of iteration.

UR - http://www.scopus.com/inward/record.url?scp=0026299757&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026299757&partnerID=8YFLogxK

M3 - Conference contribution

VL - 2

SP - 1236

EP - 1239

BT - Proceedings - IEEE International Symposium on Circuits and Systems

PB - Publ by IEEE

ER -