Singular perturbation of linear algebraic equations with application to stiff equations (Q1094821)

This paper is concerned with the existence, uniqueness and practical computation of solutions of a linear system: \(A(\epsilon)x=b(\epsilon)\) where \(\epsilon\) is a small parameter and the matrix and vector functions A(\(\epsilon)\) and b(\(\epsilon)\) are analytic in a neighborhood of the origin and A(0) is a singular matrix. This means that the problem under consideration is a singular perturbation problem of linear algebraic equations. First of all some conditions on the coefficients of the power series of A(\(\epsilon)\) and b(\(\epsilon)\) which imply the existence of a unique solution for \(| \epsilon |\) sufficiently small are given. Then the authors show how to find an approximate solution as a power series in \(\epsilon\) and obtain a bound of the error of this solution. Finally the above results are applied to solve a linear system which arises in the study of the motion of the crank guide pole mechanism of a sewing machine of type GN2.