Improved numerical stability of sparse matrix reduction method

Sparse matrix reduction is a method for solving sets of linear algebraic equations with a sparse coefficient matrix, which occur in circuit analysis. A sparse set is reduced to a much smaller full set by multiple back substitutions. No fill-ins are generated: hence the method is easily implemented and requires simple data structure and a simple algorithm. Numerical error mainly arises in the back substitution process. The error can be reduced by proper permutation of the set that maintains a narrow border of the permuted matrix, while putting the largest possible coefficients on the main diagonal of the triangular part.<>