Circuit- and graph-theoretic approach to the accuracy-guaranteed algorithm for a general-purpose circuit simulator

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Main results are the following three items :1)By using the accuracy-guaranteed algorithm developed in our laboratory we numerically proved that the specified two-transistor circuit proposed previously by other researchers has surely five solutions. As the result we see that the maximum number of solutions of two-transistor circuits is equal to or greater than five. 2) On the generation of an extremely ill-conditioned matrix 2.1) we clarified the relation between the singular values of the matrix and an upper bound of the condition number, 2.2) we proposed a new simple method to generate an extremely ill-conditioned matrix, 2.3) we proposed a method to generate a matrix with more desirable properties as the bench mark matrices for the accuracy-guaranteed algorithm. 3) We proposed several methods to estimate the upper bound of the errors of the solutions obtained by circuit analysis program such as SPICE.