The barycentric weights of rational interpolation with prescribed poles

Journal of Computational and Applied Mathematics

Volumn 86, Issue 1, 1997, Pages 45-52

  Berrut, Jean Paul ^a  

^a UNIVERSITY OF FRIBOURG   (Switzerland)

Author keywords

Barycentric representation; Interpolation; Prescribed poles; Rational interpolation

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; POLES AND ZEROS;

BARYCENTRIC REPRESENTATION;

INTERPOLATION;

EID: 0031270317     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(97)00147-7     Document Type: Article

References (19)

1. J.-P. Berrut, Baryzentrische Formeln zur trigonometrischen Interpolation (I & II), Z. Angew. Math. Phys. (ZAMP) 35 (1984) 91-105 and 193-205.
2. J.-P. Berrut, Barycentric formulae for cardinal (SINC-) interpolants, Numer. Math. 54 (1989) 703-718 (Erratum 55 (1989) 747.)
3. J.-P. Berrut, Barycentric formulae for some optimal rational approximants involving Blaschke products, Computing 44 (1990) 69-82.
4. J.-P. Berrut, Linear rational interpolation of continuous functions over an interval, in: W. Gautschi (Ed.), Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics, Proc. Symp. in Applied Mathematics, American Mathematical Society, Providence, 1994, pp. 261-264.
5. J.-P. Berrut, H. Mittelmann, Lebesgue constant minimizing linear rational interpolation of continuous functions over the interval, Comput. Math. Appl. 33 (1997) 77-86.
6. J.-P. Berrut, H. Mittelmann, Matrices for the direct determination of the barycentric weights of rational interpolation, J. Comput. Appl. Math. 78 (1997) 355-370.
7. R. Bulirsch, H. Rutishauser, Interpolation und genäherte Quadratur, in: R. Sauer, I. Szabó, (Eds.), Mathematische Hilfsmittel des Ingenieurs, Grundleriren der math. Wissenschaften, vol. 141, Springer, Berlin, 1968, pp. 232-319.
8. C. Carstensen, M. Mühlbach, The Neville-Aitken formula for rational interpolants with prescribed poles, Numer. Algorithms 3 (1992) 133-142.
9. M. Gasca, J.J. Martinez, G. Mühlbach, Computation of rational interpolants with prescribed poles, J. Comput. Appl. Math. 26 (1989) 297-309.
10. M. Golomb, Interpolation operators as optimal recovery schemes for classes of analytic functions, in: C.A. Micchelli, T.J. Rivlin (Eds.), Optimal Estimation in Approximation Theory, Plenum, New York, 1977, pp. 93-138.
11. P. Henrici, Essentials of Numerical Analysis, Wiley, New York, 1982.
12. P. Henrici, Applied and Computational Complex Analysis, vol. 3, Wiley, New York, 1986.
13. F.M. Larkin, Optimal approximation by "almost classical" interpolation, in: E.B. Saff, R.S. Varga (Eds.), Padé and Rational Approximation, Academic Press, New York, 1977, pp. 275-288.
14. G. Mühlbach, On interpolation by rational functions with prescribed poles with applications to multivariate interpolation, J. Comput. Appl. Math. 32 (1990) 203-216.
15. N. Richter-Dyn, Minimal interpolation and approximation in Hilbert spaces, SIAM J. Numer. Anal. 8 (1971) 583-597.
16. H.E. Salzer, Coefficients for facilitating trigonometric interpolation, J. Math. Phys. 27 (1948) 274-278.
17. H.E. Salzer, New formulas for trigonometric interpolation, J. Math. Phys. 39 (1960) 83-96.
18. C. Schneider, W. Werner, Some new aspects of rational interpolation, Math. Comp. 47 (1986) 285-299.
19. H. Stahl, Existence and uniqueness of rational interpolants with free and prescribed poles, in: E.B. Saff (Ed.), Approximation Theory, Tampa, Proceedings, 1985-1986, Lecture Notes in Mathematics, vol. 1287, Springer, Berlin, 1987, pp. 180-208.