### Abstract

This paper investigates the convergence property of a circuit simulation technique called an iterated timing analysis. A block strictly row-wise or column-wise diagonal dominant matrix is defined, and these matrices are shown to be nonsingular. Both block Jacobi method and block Gauss-Seidel iteration are proved to converge for the equation whose coefficient matrix is one of these matrices. On the basis of these results, the following two sufficient conditions for the iterated timing analysis to converge locally are given: (i) the capacitance matrix of the circuit is block strictly row-wise or column-wise diagonally dominant and a time step is sufficiently small, (ii) the conductance matrix of the circuit has the same property and a time step is sufficiently large.

Original language | English |
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Pages (from-to) | 1289-1293 |

Number of pages | 5 |

Journal | Transactions of the Institute of Electronics and Communication Engineers of Japan. Section E |

Volume | E69 |

Issue number | 12 |

Publication status | Published - Dec 1986 |

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### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*Transactions of the Institute of Electronics and Communication Engineers of Japan. Section E*,

*E69*(12), 1289-1293.

**SUFFICIENT CONDITIONS FOR ITERATED TIMING ANALYSIS TO CONVERGE LOCALLY.** / Urahama, Kiichi.

Research output: Contribution to journal › Article

*Transactions of the Institute of Electronics and Communication Engineers of Japan. Section E*, vol. E69, no. 12, pp. 1289-1293.

}

TY - JOUR

T1 - SUFFICIENT CONDITIONS FOR ITERATED TIMING ANALYSIS TO CONVERGE LOCALLY.

AU - Urahama, Kiichi

PY - 1986/12

Y1 - 1986/12

N2 - This paper investigates the convergence property of a circuit simulation technique called an iterated timing analysis. A block strictly row-wise or column-wise diagonal dominant matrix is defined, and these matrices are shown to be nonsingular. Both block Jacobi method and block Gauss-Seidel iteration are proved to converge for the equation whose coefficient matrix is one of these matrices. On the basis of these results, the following two sufficient conditions for the iterated timing analysis to converge locally are given: (i) the capacitance matrix of the circuit is block strictly row-wise or column-wise diagonally dominant and a time step is sufficiently small, (ii) the conductance matrix of the circuit has the same property and a time step is sufficiently large.

AB - This paper investigates the convergence property of a circuit simulation technique called an iterated timing analysis. A block strictly row-wise or column-wise diagonal dominant matrix is defined, and these matrices are shown to be nonsingular. Both block Jacobi method and block Gauss-Seidel iteration are proved to converge for the equation whose coefficient matrix is one of these matrices. On the basis of these results, the following two sufficient conditions for the iterated timing analysis to converge locally are given: (i) the capacitance matrix of the circuit is block strictly row-wise or column-wise diagonally dominant and a time step is sufficiently small, (ii) the conductance matrix of the circuit has the same property and a time step is sufficiently large.

UR - http://www.scopus.com/inward/record.url?scp=0023012621&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023012621&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0023012621

VL - E69

SP - 1289

EP - 1293

JO - Transactions of the Institute of Electronics and Communication Engineers of Japan. Section E

JF - Transactions of the Institute of Electronics and Communication Engineers of Japan. Section E

SN - 0387-236X

IS - 12

ER -