The triangular decomposition of Hankel matrices
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- by James L. Phillips PDF
- Math. Comp. 25 (1971), 559-602 Request permission
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.References
- Walter Gautschi, Construction of Gauss-Christoffel quadrature formulas, Math. Comp. 22 (1968), 251–270. MR 228171, DOI 10.1090/S0025-5718-1968-0228171-0
- Alston S. Householder, The theory of matrices in numerical analysis, Blaisdell Publishing Co. [Ginn and Co.], New York-Toronto-London, 1964. MR 0175290
- Cornelius Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Research Nat. Bur. Standards 45 (1950), 255–282. MR 0042791, DOI 10.6028/jres.045.026
- William F. Trench, An algorithm for the inversion of finite Hankel matrices, J. Soc. Indust. Appl. Math. 13 (1965), 1102–1107. MR 189232, DOI 10.1137/0113078
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Math. Comp. 25 (1971), 559-602
- MSC: Primary 65F30
- DOI: https://doi.org/10.1090/S0025-5718-1971-0295553-0
- MathSciNet review: 0295553