Abstract
This paper presents a new QRD factorization of a rectangular Vandermonde matrix for a special point distribution, including the symmetric case, based on ak-dimensional block decomposition of the matrix and some properties of the Kronecker product. The computational reduction factor with respect to any QR method isk 2, in the general case, and 4 in the symmetric one. By the resulting matrix factorization, new formulas are devised for the least squares system solution, whose implementation produces an algorithm of reduced computational cost and computer storage. Finally the perturbation bounds of this new factorization are devised.
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References
J. G. Clunie and J. C. Mason, Norms of analytic interpolation projections on general domains, J. Approx. Theory 41 (1984) 149–158.
C. J. Demeure, Fast QR factorization of Vandermonde matrices, Linear Algebra Appl. 122/123/124 (1989) 165–194.
L. Jòdar and H. Abou-Kandil, Kronecker products and coupled matrix Riccati differential systems, Linear Algebra Appl. 121 (1989) 39–51.
L. Reichel, Fast QR decomposition of Vandermonde-like matrices and polynomial least squares approximation, SIAM J. Matrix Anal. Appl. 12 (1991) 552–564.
L. Reichel, G. S. Ammar and W. B. Gragg, Discrete least squares approximation by trigonometric polynomials, Math. Comp. 57(195) (1991) 273–289.
J.-G. Sun, Perturbation bounds for the Cholesky and QR factorizations, BIT 31 (1991) 341–352.
W. P. Tang and G. H. Golub, The block decomposition of a Vandermonde matrix and its applications, BIT 21 (1981) 505–517.
T. Tommasini, A new algorithm for special Vandermonde systems, Numer. Algorithms 2 (1992) 299–306.
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Communicated by L. Reichel
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Tommasini, T. Complexity reduction of least squares problems involving special vandermonde matrices. Adv Comput Math 6, 77–86 (1996). https://doi.org/10.1007/BF02127697
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DOI: https://doi.org/10.1007/BF02127697