A matrix algorithm towards solving the moment problem of Sobolev type

Linear Algebra and Its Applications

Volumn 331, Issue 1-3, 2001, Pages 155-164

  Marcellán, Francisco ^a   Hugon Szafraniec, Franciszek ^b  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^b JAGIELLONIAN UNIVERSITY   (Poland)

Author keywords

Hankel and subhankel matrix; Hankelization and toeplitzation of a matrix; Moment problem of Sobolev type; Toeplitz and subtoeplitz matrix

Indexed keywords

EID: 0035400212     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(01)00271-3     Document Type: Article

References (11)

1. Alfaro M., Marcellán F., Rezola M.L., Ronveaux A. On orthogonal polynomials of Sobolev type: Algebraic properties and zeros. SIAM J. Math. Anal. 23:1992;737-757.
2. Barrios Rolanía D., López Lagomasino G., Pijeira Cabrera H. The moment problem for a Sobolev inner product. J. Approx. Theory. 100:1999;364-380.
3. Cachafeiro M.A., Marcellán F. Orthogonal polynomials on the unit circle. J. Approx. Theory. 78:1994;127-146.
4. Evans W.D., Littlejohn L.L., Marcellán F., Markett C., Ronveaux A. On recurrence relations for Sobolev orthogonal polynomials. SIAM J. Math. Anal. 26:1995;446-467.
5. Golub G.H., Van Loan C.F. Matrix Computations. 1989;The Johns Hopkins University Press, Baltimore.
6. Marcellán F., Alfaro M., Rezola M.L. Orthogonal polynomials on Sobolev spaces: Old and new directions. J. Comp. Appl. Math. 49:1993;225-232.
7. F. Marcellán, R. Alvarez-Nodarse, On the "Favard theorem" and their extensions, J. Comp. Appl. Math. (to appear).
8. F. Marcellán, F.H. Szafraniec, The Sobolev-type moment problem, Proc. Amer. Math. Soc. 128 (2000) 2309-2317.
9. P. Maroni, Une théorie algébrique des polynômes orthogonaux, Application aux polynômes orthogonaux semiclassiques, in: C. Brezinski, L.Gori, A. Ronveaux (Eds.), Orthogonal Polynomials and Their Applications, proceedings, Erice (Italy), June 1-6, 1990; IMACS Annals on Computing and Applied Mathematics, vol. 9, Baltzer, Basel, 1991, pp. 393-395.
10. P. Maroni, Une théorie algébrique des polynômes orthogonaux, Application aux polynômes orthogonaux semiclassiques, in: C. Brezinski, L.Gori, A. Ronveaux (Eds.), Orthogonal Polynomials and Their Applications, proceedings, Erice (Italy), June 1-6, 1990; IMACS Annals on Computing and Applied Mathematics, vol. 9, Baltzer, Basel, 1991, pp. 393-395.
11. Martínez-Finkelshtein A. Bernstein-Szegö's theorem for Sobolev orthogonal polynomials. Constr. Approx. 16:2000;73-84.