Avoiding look-ahead in the Lanczos method and Padé approximation

Volume 26 / 1999

E. Ayachour Applicationes Mathematicae 26 (1999), 33-62 DOI: 10.4064/am-26-1-33-62

Abstract

In the non-normal case, it is possible to use various look-ahead strategies for computing the elements of a family of regular orthogonal polynomials. These strategies consist in jumping over non-existing and singular orthogonal polynomials by solving triangular linear systems. We show how to avoid them by using a new method called ALA (Avoiding Look-Ahead), for which we give three principal implementations. The application of ALA to Padé approximation, extrapolation methods and Lanczos method for solving systems of linear equations is discussed.

Authors

  • E. Ayachour

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