### Abstract

Extensive studies have been carried out on the homotopy continuation algorithms which constructively determine the solution of nonlinear equations. However, their execution speed is greatly decreased when the system of equations becomes large. A decomposition method and acceleration techniques are introduced in order to improve the computational efficiency of the homotopy algorithms. A new algorithm is presented in which the system of equations is decomposed by A. K. Kevorkian's (1981) method, and then a simplicial method, which is a typical homotopy algorithm, is applied. It is shown that this algorithm has local quadratic convergence under some suitable conditions. Application of the algorithm to nonlinear two-point boundary value problems is also discussed and an efficient mesh refinement strategy is given. 10 refs.

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

Publisher | IEEE |

Pages | 635-638 |

Number of pages | 4 |

Publication status | Published - 1985 |

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### ASJC Scopus subject areas

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

### Cite this

*Proceedings - IEEE International Symposium on Circuits and Systems*(pp. 635-638). IEEE.

**DECOMPOSITION METHOD BASED ON SIMPLICIAL APPROXIMATION FOR THE NUMERICAL ANALYSIS OF NONLINEAR SYSTEMS.** / Yamamura, Kiyotaka; Horiuchi, Kazuo; Oishi, Shinichi.

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

*Proceedings - IEEE International Symposium on Circuits and Systems.*IEEE, pp. 635-638.

}

TY - GEN

T1 - DECOMPOSITION METHOD BASED ON SIMPLICIAL APPROXIMATION FOR THE NUMERICAL ANALYSIS OF NONLINEAR SYSTEMS.

AU - Yamamura, Kiyotaka

AU - Horiuchi, Kazuo

AU - Oishi, Shinichi

PY - 1985

Y1 - 1985

N2 - Extensive studies have been carried out on the homotopy continuation algorithms which constructively determine the solution of nonlinear equations. However, their execution speed is greatly decreased when the system of equations becomes large. A decomposition method and acceleration techniques are introduced in order to improve the computational efficiency of the homotopy algorithms. A new algorithm is presented in which the system of equations is decomposed by A. K. Kevorkian's (1981) method, and then a simplicial method, which is a typical homotopy algorithm, is applied. It is shown that this algorithm has local quadratic convergence under some suitable conditions. Application of the algorithm to nonlinear two-point boundary value problems is also discussed and an efficient mesh refinement strategy is given. 10 refs.

AB - Extensive studies have been carried out on the homotopy continuation algorithms which constructively determine the solution of nonlinear equations. However, their execution speed is greatly decreased when the system of equations becomes large. A decomposition method and acceleration techniques are introduced in order to improve the computational efficiency of the homotopy algorithms. A new algorithm is presented in which the system of equations is decomposed by A. K. Kevorkian's (1981) method, and then a simplicial method, which is a typical homotopy algorithm, is applied. It is shown that this algorithm has local quadratic convergence under some suitable conditions. Application of the algorithm to nonlinear two-point boundary value problems is also discussed and an efficient mesh refinement strategy is given. 10 refs.

UR - http://www.scopus.com/inward/record.url?scp=0022287706&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022287706&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0022287706

SP - 635

EP - 638

BT - Proceedings - IEEE International Symposium on Circuits and Systems

PB - IEEE

ER -