A variant algorithm of the Orthomin(m) method for solving linear systems

摘要

We propose a variant of Orthomin(m) for solving linear systems Ax=b. It is mathematically equivalent to the original Orthomin(m) method, but uses recurrence formulas that are different from those of Orthomin(m); they contain alternative expressions for the auxiliary vectors and the recurrence coefficients. Our implementation has the same computational costs as Orthomin(m). As a result of numerical experiments on nonsingular linear systems, we have confirmed the equivalence of our proposed variant of Orthomin(m) with the original Orthomin(m) using finite precision arithmetic; numerical experiments on singular linear systems show that our proposed algorithm is more accurate and less affected by rounding errors than the original Orthomin(m).