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Mathematics of Computation

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The triangular decomposition of Hankel matrices

Author: James L. Phillips
Journal: Math. Comp. 25 (1971), 559-602
MSC: Primary 65F30
MathSciNet review: 0295553
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Abstract: An algorithm for determining the triangular decomposition $ H = {R^ \ast }DR$ of a Hankel matrix H using $ O({n^2})$ operations is derived. The derivation is based on the Lanczos algorithm and the relation between orthogonalization of vectors and the triangular decomposition of moment matrices. The algorithm can be used to compute the three-term recurrence relation for orthogonal polynomials from a moment matrix.

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Keywords: Hankel matrix, triangular decomposition of matrices, orthogonalization, orthogonal polynomials, three-term recurrence relations, moment matrix, Lanczos algorithm
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society