A 1 9 / B 6 : A new lanczos-type algorithm and its implementation

Abstract

Lanczos-type algorithms are mostly derived using recurrence relationships between formal orthogonal polynomials. Various recurrence relations between these polynomials can be used for this purpose. In this paper, we discuss recurrence relations A19 and B6 for the choice Ui(x)=P(1)iUi(x)=Pi(1), where UiUi is an auxiliary family of polynomials of exact degree ii. This leads to new Lanczos-type algorithm A19/B6A19/B6 that shows superior stability when compared to existing algorithms of the same type. This new algorithm is derived and described here. Computational results obtained with it are compared to those of the most robust algorithms of this type namely A12A12,  (A^{new}_12\) A5/B10A5/B10 and A8/B10A8/B10 on the same test problems. These results are included.