Some Considerations in Solving Systems of Linear Algebraic Equations Accurately

摘要

In the paper some results concerning solving systems of linear equations accurately are presented. For fixed-precision computation using the Crout algorithm the author shows that more accurate results can be obtained if inner products are computed in backward sequences. If the inner products can be accumulated, then it is shown that accurate triangular factors L, U, and the solutions of the triangular systems can be obtained by means of a component-wise 1-shot iterative refinement procedure. Thus systems which might otherwise be declared as computationally singular may still have a chance to be solved using this approach. (Author)