An improved Lanczos algorithm for solving ill-conditioned linear equations

AbstractIn the existing Lanczos algorithms for solving systems of linear equations,the estimate for the residual is effective for well-conditioned systems. However, in actual implementation on a computer we find that the estimate is no longer reliable for ill-conditioned cases. We first analyze in theory this observation, then develop an improved Lanczos algorithm. Numerical examples are also given to demonstrate the effectiveness of the present algorithm