Chebyshev-Vandermonde systems

Authors:
Lothar Reichel and Gerhard Opfer

Journal:
Math. Comp. **57** (1991), 703-721

MSC:
Primary 65F30; Secondary 65D10

MathSciNet review:
1094957

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A Chebyshev-Vandermonde matrix

**[1]**Ȧke Björck and Victor Pereyra,*Solution of Vandermonde systems of equations*, Math. Comp.**24**(1970), 893–903. MR**0290541**, 10.1090/S0025-5718-1970-0290541-1**[2]**Philip J. Davis,*Interpolation and approximation*, Dover Publications, Inc., New York, 1975. Republication, with minor corrections, of the 1963 original, with a new preface and bibliography. MR**0380189****[3]**J. J. Dongarra, C. B. Moler, J. R. Bunch, and G. W. Stewart,*Linpack users' guide*, SIAM, Philadelphia, PA, 1979.**[4]**S. W. Ellacott,*Computation of Faber series with application to numerical polynomial approximation in the complex plane*, Math. Comp.**40**(1983), no. 162, 575–587. MR**689474**, 10.1090/S0025-5718-1983-0689474-7**[5]***Engineering and scientific subroutine library*, IBM, 1987.**[6]**Bernd Fischer and Lothar Reichel,*A stable Richardson iteration method for complex linear systems*, Numer. Math.**54**(1988), no. 2, 225–242. MR**965923**, 10.1007/BF01396976**[7]**Bernd Fischer and Lothar Reichel,*Newton interpolation in Fejér and Chebyshev points*, Math. Comp.**53**(1989), no. 187, 265–278. MR**969487**, 10.1090/S0025-5718-1989-0969487-3**[8]**Walter Gautschi and Gabriele Inglese,*Lower bounds for the condition number of Vandermonde matrices*, Numer. Math.**52**(1988), no. 3, 241–250. MR**929571**, 10.1007/BF01398878**[9]**Walter Gautschi,*The condition of Vandermonde-like matrices involving orthogonal polynomials*, Linear Algebra Appl.**52/53**(1983), 293–300. MR**709357**, 10.1016/0024-3795(83)80020-2**[10]**Walter Gautschi,*The condition of polynomials in power form*, Math. Comp.**33**(1979), no. 145, 343–352. MR**514830**, 10.1090/S0025-5718-1979-0514830-6**[11]**Walter Gautschi,*Optimally conditioned Vandermonde matrices*, Numer. Math.**24**(1975), 1–12. MR**0426401****[12]**Gene H. Golub and Charles F. Van Loan,*Matrix computations*, 2nd ed., Johns Hopkins Series in the Mathematical Sciences, vol. 3, Johns Hopkins University Press, Baltimore, MD, 1989. MR**1002570****[13]**Nicholas J. Higham,*Fast solution of Vandermonde-like systems involving orthogonal polynomials*, IMA J. Numer. Anal.**8**(1988), no. 4, 473–486. MR**975608**, 10.1093/imanum/8.4.473**[14]**Nicholas J. Higham,*Stability analysis of algorithms for solving confluent Vandermonde-like systems*, SIAM J. Matrix Anal. Appl.**11**(1990), no. 1, 23–41. MR**1032215**, 10.1137/0611002**[15]**Edmund Hlawka,*The theory of uniform distribution*, A B Academic Publishers, Berkhamsted, 1984. With a foreword by S. K. Zaremba; Translated from the German by Henry Orde. MR**750652****[16]**L. Reichel and G. Opfer,*Chebyshev-Vandermonde systems*, BSC Report 88/48, Bergen Scientific Centre, Bergen, Norway, 1988.**[17]**V. I. Smirnov and N. A. Lebedev,*Functions of a complex variable*, Iliffe Books, London, 1968.**[18]**W. P. Tang and G. H. Golub,*The block decomposition of a Vandermonde matrix and its applications*, BIT**21**(1981), no. 4, 505–517. MR**644690**, 10.1007/BF01932847

Retrieve articles in *Mathematics of Computation*
with MSC:
65F30,
65D10

Retrieve articles in all journals with MSC: 65F30, 65D10

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1991-1094957-9

Keywords:
Vandermonde-like matrix,
ordering of nodes,
numerical conditioning,
progressive algorithm,
Newton interpolation formula

Article copyright:
© Copyright 1991
American Mathematical Society