Orthogonal polynomials and the Lanczos method

C. Brezinski; H. Sadok; M. Redivo Zaglia

Displaying similar documents to “Orthogonal polynomials and the Lanczos method”

A unified approach to some strategies for the treatment of breakdown in Lanczos-type algorithms

A. El Guennouni (1999)

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The Lanczos method for solving systems of linear equations is implemented by using some recurrence relationships between polynomials of a family of formal orthogonal polynomials or between those of two adjacent families of formal orthogonal polynomials. A division by zero can occur in these relations, thus producing a breakdown in the algorithm which has to be stopped. In this paper, three strategies to avoid this drawback are discussed: the MRZ and its variants, the normalized and unnormalized...

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Two limit transitions involving multivariable BC type Askey-Wilson polynomials

Jasper Stokman (1997)

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In the first part (without proofs) an orthogonality measure with partly discrete and partly continuous support will be introduced for the five parameter family of multivariable BC type Askey-Wilson polynomials. In the second part, the limit transitions from BC type Askey-Wilson polynomials to BC type big and little q-Jacobi polynomials will be described in detail.

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Beiträge zur Algebra und Geometrie

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Linearization of the product of orthogonal polynomials of a discrete variable

Saïd Belmehdi, Stanisław Lewanowicz, André Ronveaux (1997)

Applicationes Mathematicae

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Let $P_{k}$ be any sequence of classical orthogonal polynomials of a discrete variable. We give explicitly a recurrence relation (in k) for the coefficients in $P_{i} P_{j} = \sum_{k} c (i, j, k) P_{k}$ , in terms of the coefficients σ and τ of the Pearson equation satisfied by the weight function ϱ, and the coefficients of the three-term recurrence relation and of two structure relations obeyed by $P_{k}$ .