Abstract
We propose a variant of the ORTHOMIN (m) method 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. Also, our proposed algorithm has the same computational costs as ORTHOMIN (m). Through numerical experiments on nonsingular linear systems we confirm the equivalence on numerical computations with finite precision arithmetic, and numerical experiments on singular linear systems show that our proposed algorithm is more accurate and less affected by rounding errors than the original.
