Exponential convergence of a linear rational interpolant between transformed Chebyshev points

Mathematics of Computation

Volumn 68, Issue 227, 1999, Pages 1109-1120

  Baltensperger, Richard ^a   Berrut, Jean Paul ^b   Noël, Benjamin ^b  

^a UNIVERSITY OF FRIBOURG   (Switzerland)

^b NONE

Author keywords

Exponential convergence; Interpolation; Linear interpolation; Rational interpolation

Indexed keywords

EID: 0039982139     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-99-01070-4     Document Type: Article

References (27)

1. Baltensperger, R. and Berrut, J.-P.: The errors in calculating the pseudospectral differentiation matrices for Chebyshev-Gauss-Lobatto points, to appear in Comput. Math. Applic.
2. Baltensperger, R. and Berrut, J.-P.: The linear rational collocation method, submitted for publication.
3. Berrut, J.-P.: Rational functions for guaranteed and experimentally well-conditioned global interpolation, Comput. Math. Applic., 15, 1-16 (1988). MR 89b:65029
4. Berrut, J.-P.: Rational functions for guaranteed and experimentally well-conditioned global interpolation, Comput. Math. Applic., 15, 1-16 (1988). MR 89b:65029
5. Berrut, J.-P.: Barycentric formulae for cardinal (SINC-) interpolants, Numer. Math., 54, 703-718 (1989) (Erratum 55, 747 (1989)). MR 90d:65025a,b
6. Berrut, J.-P.: Barycentric formulae for cardinal (SINC-) interpolants, Numer. Math., 54, 703-718 (1989) (Erratum 55, 747 (1989)). MR 90d:65025a,b
7. Berrut, J.-P. and Mittelmann, H. D.: Lebesgue constant minimizing linear rational interpolation of continuous functions over the interval, Comput. Math. Applic., 33, 77-86 (1997). MR 98c:41015
8. Berrut, J.-P. and Mittelmann, H. D.: Lebesgue constant minimizing linear rational interpolation of continuous functions over the interval, Comput. Math. Applic., 33, 77-86 (1997). MR 98c:41015
9. Boyd, J. P.: Chebyshev and Fourier Spectral Methods, Springer Verlag, Berlin-Heidelberg-New York (1989).
10. Henrici, P.: Essentials of Numerical Analysis with Pocket Calculator Demonstrations, Wiley, New York (1982). MR 83h:65002
11. Henrici, P.: Essentials of Numerical Analysis with Pocket Calculator Demonstrations, Wiley, New York (1982). MR 83h:65002
12. Kaup, L. and Kaup, B.: Holomorphic Functions of Several Variables, de Gruyter, Berlin-New York (1983). MR 85k:32001
13. Kaup, L. and Kaup, B.: Holomorphic Functions of Several Variables, de Gruyter, Berlin-New York (1983). MR 85k:32001
14. -1) time step restriction, J. Comput. Phys., 104, 457-469 (1993). MR 93k:65080
15. -1) time step restriction, J. Comput. Phys., 104, 457-469 (1993). MR 93k:65080
16. Rivlin, T. J.: The Chebyshev Polynomials, Wiley, New York (1974). MR 56:9142
17. Rivlin, T. J.: The Chebyshev Polynomials, Wiley, New York (1974). MR 56:9142
18. n,v = cos(vπ/n), v = 0(1)n; some unnoted advantages, The Computer J., 15, 156-159 (1972). MR 47:4414
19. n,v = cos(vπ/n), v = 0(1)n; some unnoted advantages, The Computer J., 15, 156-159 (1972). MR 47:4414
20. Schneider, C. and Werner, W.: Some new aspects of rational interpolation, Math. Comp., 47, 285-299 (1986). MR 87k:65012
21. Schneider, C. and Werner, W.: Some new aspects of rational interpolation, Math. Comp., 47, 285-299 (1986). MR 87k:65012
22. Schwarz, H. R.: Numerische Mathematik, 2te Aufl., Teubner, Stuttgart (1988); English translation: Numerical Analysis, A Comprehensive Introduction, Wiley, New-York (1989). MR. 92a:65008; MR 90g:65003
23. Schwarz, H. R.: Numerische Mathematik, 2te Aufl., Teubner, Stuttgart (1988); English translation: Numerical Analysis, A Comprehensive Introduction, Wiley, New-York (1989). MR. 92a:65008; MR 90g:65003
24. Schwarz, H. R.: Numerische Mathematik, 2te Aufl., Teubner, Stuttgart (1988); English translation: Numerical Analysis, A Comprehensive Introduction, Wiley, New-York (1989). MR. 92a:65008; MR 90g:65003
25. Schwarz, H. R.: Numerische Mathematik, 2te Aufl., Teubner, Stuttgart (1988); English translation: Numerical Analysis, A Comprehensive Introduction, Wiley, New-York (1989). MR. 92a:65008; MR 90g:65003
26. Stoer, J.: Einführung in die Numerische Mathematik I, 4te Aufl., Springer, Berlin (1983). MR 83d:65003 (3rd ed.)
27. Stoer, J.: Einführung in die Numerische Mathematik I, 4te Aufl., Springer, Berlin (1983). MR 83d:65003 (3rd ed.)