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Various recurrence relations between formal orthogonal polynomials can be used to derive Lanczos-type algorithms. In this paper, we
consider recurrence relation A12 for the choice Ui(x) = Pi(x), where
Ui
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 A12, A5/B10 and A8/B10, on the same test
problems. Numerical results are included.
Saifullah, Muhammad Farooq, Abdellah Salhi. (2013) An alternative derivation of a new Lanczos-type algorithm for systems of linear equations, , Volume 45, Issue 1.
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