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Vector Stieltjes Continued Fraction and Vector QD Algorithm

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Abstract

The definition, in previous studies, of vector Stieltjes continued fractions in connexion with spectral properties of band operators with intermediate zero diagonals, left unsolved the question of a direct definition of their coefficients in terms of the original data, a vector of Stieltjes series. A new version of the vector QD algorithm allows to extend to the vector case the result which was known for one scalar function. Beside this connexion, it solves the inverse Miura transform and gives interesting identities between general band matrix and sparse band matrix. It gives also some effective computations of coefficients linked to vector orthogonality.

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Authors and Affiliations

  1. UFR de Mathématiques, Université de Lille, 59655, Villeneuve d'Ascq Cedex, France

    Jeannette Van Iseghem

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  1. Jeannette Van Iseghem
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Van Iseghem, J. Vector Stieltjes Continued Fraction and Vector QD Algorithm. Numerical Algorithms 33, 485–498 (2003). https://doi.org/10.1023/A:1025565400379

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  • DOI: https://doi.org/10.1023/A:1025565400379

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