### Abstract

This paper investigates convergence properties of a circuit simulation technique called Waveform Relaxation (WR). A general formulation of a family of WR algorithms called a generalized WR is introduced. This formulation reduces to some introduced WR algorithms in particular cases. The following two sufficient conditions for the generalized WR method to converge locally are given: i) the capacitance matrix of the circuit is block strictly diagonally dominant and a time-steplength is sufficiently small; ii) the conductance matrix of the circuit has the same property and a time-steplength is sufficiently large.

Original language | English |
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Pages (from-to) | 106-109 |

Number of pages | 4 |

Journal | Transactions of the Institute of Electronics, Information and Communication Engineers, Section E ( |

Volume | E70 |

Issue number | 2 |

Publication status | Published - Feb 1 1987 |

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### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

**SUFFICIENT CONDITIONS FOR A GENERALIZED WAVEFORM RELAXATION TO CONVERGE LOCALLY.** / Urahama, Kiichi.

Research output: Contribution to journal › Article

*Transactions of the Institute of Electronics, Information and Communication Engineers, Section E (*, vol. E70, no. 2, pp. 106-109.

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TY - JOUR

T1 - SUFFICIENT CONDITIONS FOR A GENERALIZED WAVEFORM RELAXATION TO CONVERGE LOCALLY.

AU - Urahama, Kiichi

PY - 1987/2/1

Y1 - 1987/2/1

N2 - This paper investigates convergence properties of a circuit simulation technique called Waveform Relaxation (WR). A general formulation of a family of WR algorithms called a generalized WR is introduced. This formulation reduces to some introduced WR algorithms in particular cases. The following two sufficient conditions for the generalized WR method to converge locally are given: i) the capacitance matrix of the circuit is block strictly diagonally dominant and a time-steplength is sufficiently small; ii) the conductance matrix of the circuit has the same property and a time-steplength is sufficiently large.

AB - This paper investigates convergence properties of a circuit simulation technique called Waveform Relaxation (WR). A general formulation of a family of WR algorithms called a generalized WR is introduced. This formulation reduces to some introduced WR algorithms in particular cases. The following two sufficient conditions for the generalized WR method to converge locally are given: i) the capacitance matrix of the circuit is block strictly diagonally dominant and a time-steplength is sufficiently small; ii) the conductance matrix of the circuit has the same property and a time-steplength is sufficiently large.

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UR - http://www.scopus.com/inward/citedby.url?scp=0023296046&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0023296046

VL - E70

SP - 106

EP - 109

JO - Transactions of the Institute of Electronics, Information and Communication Engineers, Section E (

JF - Transactions of the Institute of Electronics, Information and Communication Engineers, Section E (

IS - 2

ER -