Ratio Asymptotics for Orthogonal Matrix Polynomials

Journal of Approximation Theory

Volumn 100, Issue 2, 1999, Pages 304-344

  Duran, Antonio J ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Ratio asymptotics; quadrature formulae; orthogonal matrix polynomials; Chebyshev polynomials

Indexed keywords

EID: 0000169130     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1999.3351     Document Type: Article

References (20)

1. Aptekarev A. I., Nikishin E. M. The scattering problem for a discrete Sturm-Liouville operator. Mat. Sb. 121:1983;327-358.
2. Basu S., Bose N. K. Matrix Stieltjes series and network models. Siam J. Math. Anal. 14:1983;209-222.
3. Duran A. J. Ratio asymptotics and quadrature formulas. Constr. Approx. 13:1997;271-286.
4. Duran A. J. A generalization of Favard's Theorem for polynomials satisfying a recurrence relation. J. Approx. Theory. 74:1993;83-109.
5. Duran A. J. On orthogonal polynomials with respect to a positive definite matrix of measures. Canad. J. Math. 47:1995;88-112.
6. Duran A. J. Markov theorem for orthogonal matrix polynomials. Canad. J. Math. 48:1996;1180-1195.
7. Duran A. J., Lopez-Rodriguez P. Orthogonal matrix polynomials: Zeros and Blumenthal's theorem. J. Approx. Theory. 84:1996;96-118.
8. Duran A. J., Van Assche W. Orthogonal polynomials and higher order recurrence relations. Linear Algebra Appl. 219:1995;261-280.
9. Geronimo J. S., Van Assche W. Orthogonal polynomials with asymptotically periodic recurrence coefficients. J. Approx. Theory. 46:1986;251-283.
10. Gohberg I., Lancaster P., Rodman L. Matrix Polynomials. 1982;Academic Press, New York.
11. Horn R. A., Johnson C. R. Matrix Analysis. 1985;Cambridge Univ. Press, Cambridge.
12. Horn R. A., Johnson C. R. Topics in Matrix Analysis. 1991;Cambridge Univ. Press, Cambridge.
13. N. Jacobson, Basic Algebra I, Freeman, San Francisco.
14. Máté A., Nevai P., Van Assche W. The supports of measures associated with orthogonal polynomials and the spectra of the related self-adjoint operators. Rocky Mt. J. Math. 21:1991;501-527.
15. Nevai P. G. Orthogonal Polynomials. 1979;Am. Math. Soc. Providence.
16. Rellich F. Perturbation Theory of Eigenvalue Problems. 1969;Gordon & Breach, New York.
17. Sinap A., Van Assche W. Polynomials interpolation and Gaussian quadrature for matrix-valued functions. Linear Algebra Appl. 207:1994;71-114.
18. Van Assche W. Asymptotics for Orthogonal Polynomials. Lecture Notes in Mathematics. 1265:1987;Springer-Verlag, Berlin/New York.
19. Van Assche W. The ratio of q-like orthogonal polynomials. J. Math. Anal. Appl. 128:1987;535-547.
20. Van Assche W. Asymptotic properties of orthogonal polynomials from their recurrence formula, I. J. Approx. Theory. 44:1985;258-276.