Pin-pointing solution of ill-conditioned square systems of linear equations
Konstantin Volokh, Oren Vilnay · Applied Mathematics Letters · 2000
A new method is proposed for an accurate solution of nearly singular systems of linear equations. The method uses the truncated singular value decomposition of the initial coefficient matrix at the first stage and the Gaussian elimination procedure for a well-conditioned reduced system of linear equations at the last stage. In contrast to various regularization techniques, the method does not require any additional physical information on the problem.