Fast algorithms of Björck-Pereyra type for solving Cauchy-Vandermonde linear systems

Applied Numerical Mathematics

Volumn 26, Issue 3, 1998, Pages 343-352

  Martinez J J ^a   Pena J M ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

Cauchy Vandermonde matrices; Linear systems; Rational interpolation; Total positivity

Indexed keywords

ALGORITHMS; INTERPOLATION; PROBLEM SOLVING;

BJORCK-PEREYRA ALGORITHM; CAUCHY-VANDERMONDE LINEAR SYSTEMS; RATIONAL INTERPOLATION;

MATRIX ALGEBRA;

EID: 0032017488     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(97)00102-5     Document Type: Article

References (18)

1. T. Ando, Totally positive matrices, Linear Algebra Appl. 90 (1987) 165-219.
2. A. Björck and V. Pereyra, Solution of Vandermonde systems of equations, Math. Comp. 24 (1970) 893-903.
3. T. Boros, T. Kailath and V. Olshevsky, The fast Björck-Pereyra-type algorithm for Cauchy linear systems, Preprint.
4. J.M. Carnicer and J.M. Peña, Totally positive bases for shape preserving curve design and optimality of B-splines, Computer Aided Geometric Design 11 (1994) 633-654.
5. J.M. Carnicer and J.M. Peña, On transforming a Tchebycheff system into a strictly totally positive system, J. Approx. Theory 81 (1995) 274-295.
6. J.M. Carnicer and J.M. Peña, Characterizations of the optimal Descartes' rules of signs, Math. Nachr., to appear.
7. C. Carstensen and G. Mülbach, The Neville-Aitken formula for rational interpolations with prescribed poles, Numer. Algorithms 3 (1992) 133-142.
8. T. Finck, G. Heinig and K. Rost, An inversion formula and fast algorithms for Cauchy-Vandermonde matrices, Linear Algebra Appl. 183 (1993) 179-191.
9. M. Gasca and J.J. Martínez, On the computation of multivariate confluent Vandermonde determinants and its applications, in: R. Martin, ed., The Mathematics of Surfaces II (Oxford University Press, Oxford, 1987) 101-114.
10. M. Gasca, J.J. Martínez and G. Mülbach, Computation of rational interpolants with prescribed poles, J. Comput. Appl. Math. 26 (1989) 297-309.
11. G.H. Golub and C.F. Van Loan, Matrix Computations (Johns Hopkins University Press, Baltimore, MD, 3rd ed., 1996).
12. P. Junghanns and D. Oestreich, Numerische Lösung des Staudammproblems mit Drainage, Z. Angew. Math. Mech. 69 (1989) 83-92.
13. S. Karlin, Total Positivity, Vol. I (Stanford University Press, Stanford, CA, 1968).
14. G. Mülbach, Computation of Cauchy-Vandermonde determinants, J. Number Theory 43 (1993) 74-81.
15. G. Mülbach, On Hermite interpolation by Cauchy-Vandermonde systems: the Lagrange formula, the adjoint and the inverse of a Cauchy-Vandermonde matrix, J. Comput. Appl. Math. 67 (1996) 147-159.
16. G. Mülbach and L. Reimers, Linear extrapolation by rational functions, exponentials and logarithmic functions, J. Comput. Appl. Math. 17 (1987) 329-344.
17. V. Pan, On computations with dense structured matrices, Math. Comp. 55 (1990) 179-190.
18. O. Taussky and M. Marcus, Eigenvalues of finite matrices, in: J. Todd, ed., Survey of Numerical Analysis (McGraw-Hill, New York, 1962) 279-313.