The use of small pivot perturbation in circuit analysis

A technique that can improve the accuracy of Gaussian elimination in those cases where small pivot magnitudes are encountered during the Gaussian elimination procedure, thus avoiding an inaccurate solution and allowing the analysis to continue, is presented. This technique is known as small pivot perturbation (SPP). It is shown that SPP can be used to provide accurate solutions in those cases where Gaussian elimination without row or column pivoting has resulted in a very small or zero-valued pivot. The SPP technique has been implemented in the AS/X circuit analysis program. For the AS/X circuit analysis application, where maintenance of matrix sparsity has ruled out any pivoting during Gaussian elimination, SPP is the most practical technique yet found for dealing with small pivots