### Abstract

Zukowski's theorem on a monotone convergence of Waveform Relaxation (WR) is generalized. The sequence of iterated waveforms in the WR method is proven to converge monotonically for a system where the time derivative of variables reduces to a quasi-monotone increasing function by a linear transformation of the variables. This result is applied to a class of MOS digital circuits, and a sufficient condition on the topology of the circuit and input waveforms is derived such that the sequence of iterated waveforms in the WR method applied to the circuit converges monotonically.

Original language | English |
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Pages (from-to) | 407-410 |

Number of pages | 4 |

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

Volume | E70 |

Issue number | 4 |

Publication status | Published - Apr 1 1987 |

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### All Science Journal Classification (ASJC) codes

- Engineering(all)