### 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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Pages (from-to) | 1236-1239 |

Number of pages | 4 |

Journal | Proceedings - IEEE International Symposium on Circuits and Systems |

Volume | 2 |

Publication status | Published - 1991 Dec 1 |

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 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

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## Cite this

Oishi, S., Kashiwagi, M., Makino, M., & Horiuchi, K. (1991). An Urabe type convergence theorem for a constructive simplified Newton method in infinite dimensional spaces.

*Proceedings - IEEE International Symposium on Circuits and Systems*,*2*, 1236-1239.