When computing recursively the members of a family of formal orthogonal polynomials, a division by zero can occur, thus producing a breakdown in the algorithm which has to be stopped. In this paper, such breakdowns are analyzed in detail and classified. It is also showed how to avoid them in some particular cases. Applications to Padé approximations, extrapolation methods and Lanczos method for solving systems of linear equations are discussed.
Breakdowns in the computation of Orthogonal Polynomials
REDIVO ZAGLIA, MICHELA
1994
Abstract
When computing recursively the members of a family of formal orthogonal polynomials, a division by zero can occur, thus producing a breakdown in the algorithm which has to be stopped. In this paper, such breakdowns are analyzed in detail and classified. It is also showed how to avoid them in some particular cases. Applications to Padé approximations, extrapolation methods and Lanczos method for solving systems of linear equations are discussed.
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