An alternative derivation of a new Lanczos-type algorithm for systems of linear equations

Various recurrence relations between formal orthogonal polynomials can be used to derive Lanczos-type algorithms. In this paper, we consider recurrence relation A(12) for the choice U-i (x) = P-i (x), where U(i )is an auxiliary family of polynomials of exact degree i. It leads to a Lanczos-type algorithm that shows superior stability when compared to existing Lanczos-type algorithms. The new algorithm is derived and described. It is then computationally compared to the most robust algorithms of this type, namely A(12), A(5)/B-10 and A(8)/B-10, on the same test problems. Numerical results are included.