SUFFICIENT CONDITIONS FOR ITERATED TIMING ANALYSIS TO CONVERGE LOCALLY.

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.