The stable computation of formal orthogonal polynomials

Numerical Algorithms

Volumn 11, Issue 1, 1996, Pages 1-23

  Beckermann, Bernhard ^a  

^a UNIV LILLE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21344435014     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02142485     Document Type: Article

References (9)

1. B. Beckermann, On the numerical condition of polynomial bases: Estimates for the condition number of Vandermonde, Krylov and Hankel matrices, to appear.
2. J.R. Bunch, The weak and the strong stability of algorithms in numerical linear algebra, Lin. Alg. Appl. 88/89 (1987) 49-66.
3. S. Cabay and R. Meleshko, A weakly stable algorithm for Padé approximants and the inversion of Hankel matrices, SIAM J. Matrix Anal. Appl. 14 (1993) 735-765.
4. W. Daniel, W.B. Gragg, L. Kaufmann and G.W. Stewart, Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization, Math. Comp. 30 (1976) 772-795.
5. G.H. Golub and C.F. Van Loan, Matrix Computations, 2nd ed. (Johns Hopkins University Press, Baltimore/London, 1993).
6. M.H. Gutknecht and W.B. Gragg, Stable look-ahead versions of the Euclidean and Chebyshev algorithms, in: Approximation and Computation, Proceedings Purdue 1993, ed. R.M.V. Zahar, ISNM 119 (Birkhäuser, Boston, 1994).
7. G. Heinig and K. Rost, Algebraic Methods for Toeplitz-like Matrices and Operators (Akademie Verlag, Berlin, 1984).
8. J.M. Varah, Backward error estimation for Toeplitz systems, SIAM J. Matrix Anal. Appl. 15 (1994) 408-417.
9. J.H. Wilkinson, The Algebraic Eigenvalue Problem (Clarendon Press, Oxford, 1965).