Orthogonal polynomials (in Matlab)

Journal of Computational and Applied Mathematics

Volumn 178, Issue 1-2 SPEC. ISS., 2005, Pages 215-234

  Gautschi, Walter ^a  

^a Purdue University   (United States)

Author keywords

Matlab; Orthogonal polynomials; Recurrence relations

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; LEAST SQUARES APPROXIMATIONS; MATRIX ALGEBRA; METHOD OF MOMENTS;

ORTHOGONAL POLYNOMIALS; RECURRENCE RELATIONS;

POLYNOMIALS;

EID: 14844341327     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.03.029     Document Type: Article

References (28)

1. P. Althammer Eine Erweiterung des Orthogonalitätsbegriffes bei Polynomen und deren Anwendung auf die beste Approximation J. Reine Angew. Math. 211 1962 192-204
2. P.L. Chebyshev, Sur l'interpolation par la méthode des moindres carrés, Mem. Acad. Impér. Sci. St. Petersbourg (7)1(15) (1859) 1-24. Also in Œuvres I, pp. 473-498.
3. T.S. Chihara An introduction to orthogonal polynomials Mathematics and Its Applications vol. 13 1978 Gordon and Breach New York
4. B. Fischer G.H. Golub How to generate unknown orthogonal polynomials out of known orthogonal polynomials J. Comput. Appl. Math. 43 1992 99-115
5. G. Freud Orthogonal Polynomials 1971 Pergamon Press New York (English translation of Orthogonale Polynome, Birkhäuser, Basel, 1969.)
6. D. Galant An implementation of Christoffel's theorem in the theory of orthogonal polynomials Math. Comp. 25 1971 111-113
7. W. Gautschi Construction of Gauss-Christoffel quadrature formulas Math. Comp. 22 1968 251-270
8. W. Gautschi, An algorithmic implementation of the generalized Christoffel theorem, in: G. Hämmerlin (Ed.), Numerical Integration, Internat. Ser. Numer. Math. 57 (1982) 89-106, Birkhäuser, Basel.
9. W. Gautschi On generating orthogonal polynomials SIAM J. Sci. Statist. Comput. 3 1982 289-317
10. W. Gautschi On some orthogonal polynomials of interest in theoretical chemistry BIT 24 1984 473-483
11. W. Gautschi Algorithm 726: ORTHPOL-a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules ACM Trans. Math. Software 20 1994 21-62
12. W. Gautschi The interplay between classical analysis and (numerical) linear algebra-a tribute to Gene H. Golub Electron. Trans. Numer. Anal. 13 2002 119-147
13. W. Gautschi Orthogonal Polynomials: Computation and Approximation 2004 Oxford University Press Oxford
14. W. Gautschi S. Li A set of orthogonal polynomials induced by a given orthogonal polynomial Aequationes Math. 46 1993 174-198
15. W. Gautschi M. Zhang Computing orthogonal polynomials in Sobolev spaces Numer. Math. 71 1995 159-183
16. W.B. Gragg W.J. Harrod The numerically stable reconstruction of Jacobi matrices from spectral data Numer. Math. 44 1984 317-335
17. J. Kautsky G.H. Golub On the calculation of Jacobi matrices Linear Algebra Appl. 52/53 1983 439-455
18. C. Lanczos An iteration method for the solution of the eigenvalue problem of linear differential and integral operators J. Res. Nat. Bur. Standards 45 1950 255-282, Also in Collected Published Papers with Commentaries, vol. V pp. 3-9-3-36.
19. 1(x), Report AECL-3461, Atomic Energy of Canada Limited, Chalk River, Ontario, 1969.
20. H. Rutishauser, On Jacobi rotation patterns, in: N.C. Metropolis, A.H. Taub, J. Todd, C.B. Tompkins (Eds.), Experimental Arithmetics, High Speed Computing and Mathematics, Proc. Sympos. Appl. Math. 15 (1963) 219-239, American Mathematical Society, Providence, RI.
21. R.A. Sack A.F. Donovan An algorithm for Gaussian quadrature given modified moments Numer. Math. 18 1972 465-478
22. H. Stahl V. Totik General orthogonal polynomials Encyclopedia of Mathematics and Its Applications vol. 43 1992 Cambridge University Press Cambridge
23. T.J. Stieltjes, Quelques recherches sur la théorie des quadratures dites mécaniques, Ann. Sci. École Norm. Paris (3)1 (1884) 409-426. Also in Œuvres I, pp. 377-396.
24. P.K. Suetin Classical Orthogonal Polynomials second ed. 1979 Nauka Moscow (in Russian)
25. G. Szegö, Orthogonal Polynomials, fourth ed., AMS Colloquium Publications, vol. 23, American Mathematical Society, Providence, RI, 1975.
26. J.C. Wheeler Modified moments and Gaussian quadratures Rocky Mountain J. Math. 4 1974 287-296
27. R. Wong Quadrature formulas for oscillatory integral transforms Numer. Math. 39 1982 351-360
28. M. Zhang, Sensitivity analysis for computing orthogonal polynomials of Sobolev type, in: R.V.M. Zahar (Ed.), Approximation and computation, Internat. Ser. Numer. Math. 119 (1994) 563-576, Birkhäuser Boston, Boston, MA.