Symmetric functions and the Vandermonde matrix

Journal of Computational and Applied Mathematics

Volumn 172, Issue 1, 2004, Pages 49-64

  Oruç, Halil ^a   Akmaz, Hakan K ^a  

^a DOKUZ EYLUL UNIVERSITY   (Turkey)

Author keywords

Q Stirling numbers; Symmetric functions; Triangular and bidiagonal factorization; Vandermonde matrix

Indexed keywords

FUNCTIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA;

COMBINATORIAL IDENTITIES; VANDERMONDE MATRIX;

COMPUTATIONAL METHODS;

MATHEMATICAL METHOD;

EID: 4444382694     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.01.032     Document Type: Article

References (25)

1. Andrews G.E. The Theory of Partitions 1998 Cambridge University Press Cambridge
2. Björck A. Pereyra V. Solution of Vandermonde systems of equations Math. Comp. 24 1970 893-903
3. Cheon G.S. Kim J.S. Stirling matrix via Pascal matrix Linear Algebra Appl. 329 2001 49-59
4. Eisinberg A. Franzé G. Pugliese P. Vandermonde matrices on integer nodes Numer. Math. 80 1998 75-85
5. Eisinberg A. Pugliese P. Salerno N. Vandermonde matrix on integer nodes: the rectangular case Numer. Math. 87 2001 663-674
6. Gohberg I. Koltracht I. Triangular factors of Cauchy and Vandermonde matrices Integral Equations Oper. Theory 26 1996 46-59
7. Gohberg I. Olshevsky V. The fast generalized Parker-Traub algorithm for inversion of Vandermonde and related matrices J. Complexity 13 1997 208-234
8. Goodman T.N.T. Total positivity and shape of curves Gasca M. Micchelli C.A. Total Positivity and its Applications 1996 157-186 Kluwer Academic Publisher Dordrecht
9. Goodman T.N.T. Oruç H. Phillips G.M. Convexity and generalized Bernstein polynomials Proc. Edin. Math. Soci. 42 1999 179-190
10. Gould H.W. The q-Stirling numbers of the first kind and the second kind Duke Math. J. 28 1961 281-289
11. D.E. Knuth, The Art of Computer Programming, Vol. 1, Addison-Wesley, Reading, MA, 1973.
12. Konvalin J. Generalized-binomial coefficients and the subset-subspace problem Adv. Appl. Math. 21 1998 228-240
13. MacDonald I.G. Symmetric Functions and Hall Polynomials 1979 Clarendon Press Oxford
14. Mart́nez J.J. Pena J.M. Factorization of Cauchy-Vandermonde matrices Linear Algebra Appl. 284 1998 229-237
15. Mart́nez J.J. Pena J.M. Fast algorithms of Björck-Pereyra type for solving Cauchy-Vandermonde linear systems Appl. Num. Math. 26 1998 343-352
16. H. Oruç, The generalized Bernstein polynomials and total positivity, Ph.D. Thesis, University of St. Andrews, 1998
17. http://web.deu.edu.tr/halil.oruc/
18. Oruç H. Phillips G.M. Explicit factorization of the Vandermonde matrix Linear Algebra Appl. 315 2000 113-123
19. Oruç H. Phillips G.M. q-Bernstein polynomials and Bézier curves J. Comput. Appl. Math. 151 2003 1-12
20. Oruç H. Tuncer N. On the convergence and iterates of q-Bernstein polynomials J. Approx. Theory 117 2002 301-313
21. Phillips G.M. Two Millenia of Mathematics from Archimedes to Gauss 2000 Springer New York
22. Phillips G.M. Interpolation and Approximation by Polynomials 2003 Springer New York
23. Schumaker L.L. Spline Functions: Basic Theory 1981 Wiley
24. R.P. Stanley, Enumerative Combinatorics, Vol. 2, Cambridge University Press, Cambridge, MA, 1999.
25. Zhizheng Z. The linear algebra of the generalized Pascal matrix Linear Algebra Appl. 250 1997 51-60