A New Method of Solving Ill-Conditioned Systems of Equations

摘要

The problems associated with ill-conditioned matrices are well known and widespread. As of yet, there are no general solutions to the problem. The only remedies are usually ad hoc and are extremely case-dependent. This paper presents a method which gives good results for a large variety of situations. The method involves masking, a technique which sets the lower-order bits (the number of bits varies) to zero, and then applying standard system-of-equations solvers. Most of the computer runs made used the Hilbert matrix, and either a specified b vector (as in the form, Ax = b), or a specified x vector, with the b obtained by multiplying x by A. (Author)