Abstract
Matrices are investigated that are Hankel matrices in bases of orthogonal polynomials. With the help of 3 equivalent definitions of this class fast LU-factorization algorithms and superfast solvers are con-structed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Dutt, A., Rokhlin, V.: Fast Fourier transforms for nonequispaced data. SIAM J. Sci. Comp. 14 (1993) 1368–1393
Fasino, D.: Preconditioning finite moment problems. J. Comp. Appl. Math. 65(1995) 145–155
Gemignani, L.: A fast algorithm for generalized Hankel matrices arising in finite-moment problems. Linear Algebra Appl. 267 (1997) 41–52
Golub, G., Gutknecht, M.: Modified moments for indefinite weight functions. Nu-mer. Math. 67 (1994) 71–92
Gustafson, S. A.: On computational applications of the theory of moment problems. Rocky Mountain J. Math. 2 (1974) 227–240
Heinig, G.: Chebyshev-Hankel matrices and the splitting approach for centrosym-metric Toeplitz-plus-Hankel matrices. Linear Algebra Appl. (to appear)
Heinig, G., Bojanczyk, A.: Transformation techniques for Toeplitz and Toeplitz-plus-Hankel matrices, I. Transformations: Linear Algebra Appl. 254 (1997) 193–226, II. Algorithms: Linear Algebra Appl. 278 (1998), 11-36
Heinig, G., Hoppe, W., Rost, K.: Structured matrices in interpolation and ap-proximation problems, Wissensch. Zeitschr. d. TU Karl-Marx-Stadt 31 2 (1989) 196–202
Heinig, G., Olshevsky, V.: The Schur algorithm for matrices with Hessenberg dis-placement structure. (in preparation)
Heinig, G., Rost, K.: Algebraic Methods for Toeplitz-like matrices and operators. Akademie-Verlag Berlin and Birkhäuser Basel, Boston, Stuttgart, 1984
Kailath, T., Sayed, A.: Displacement structure: Theory and applications. SIAM Revue 37 (1995) 297–386
Olshevsky, V., Pan, V.: A unified superfast algorithm for boundary rational tangen-tial interpolation problems and for inversion and factorization of dense structured matrices. Proc. of 39th Annual IEEE Symposium on Foundation of Computer Science1998, 192–201
Potts, D., Steidl, G., Tasche, M.: Fast algorithms for discrete polynomial trans-forms. Math.Comp. 67 224 (1998) 1577–1599
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Heinig, G. (2001). Fast and Superfast Algorithms for Hankel-Like Matrices Related to Orthogonal Polynomials. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_45
Download citation
DOI: https://doi.org/10.1007/3-540-45262-1_45
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41814-6
Online ISBN: 978-3-540-45262-1
eBook Packages: Springer Book Archive