An alternative to Chan's deflation for bordered systems

Publisher Website
Google Scholar
Abstract
In many contexts, notably in computing continuation curves near singular points, it is necessary to solve linear systems of the form[EQUATION]where A is n x n , b is n x 1, c is 1 x n , and d is a scalar. (Thus x, f are n -vectors and y, g are scalars.) The complete ( n + 1) x ( n + 1) matrix M is assumed to be well-conditioned, but A is expected to be singular or nearly so. In addition A is assumed to possess useful properties which may be lost if the augmented matrix M is dealt with directly: e.g. A might have a band structure which would be lost by pivoting too soon in the bottom row. Thus for efficiency's sake we wish to use a solver for systems with coefficient matrix A , but its likely ill-condition demands special care.

This publication has 1 reference indexed in Scilit: