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Prony’s method for completely monotonic functions. (English) Zbl 0357.65005


MSC:

65D05 Numerical interpolation
41A30 Approximation by other special function classes
41A25 Rate of convergence, degree of approximation
11L03 Trigonometric and exponential sums (general theory)
41A05 Interpolation in approximation theory
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References:

[1] Braess, D., Rationale Interpolation, Normalität und Monosplines, Numer. Math., 22, 219-232 (1974) · Zbl 0281.65005
[2] Davis, P. J., Interpolation and Approximation (1963), Blaisdell: Blaisdell Waltham, Mass · Zbl 0111.06003
[3] Hamming, R. W., Numerical Methods for Scientists and Engineers (1962), McGraw-Hill: McGraw-Hill New York · Zbl 0952.65500
[4] Hildebrand, F. B., Introdution to Numerical Analysis (1974), McGraw-Hill: McGraw-Hill New York · Zbl 0279.65001
[5] Kammler, D. W., Approximation with sums of exponentials in \(L_p\)[0, ∞], J. Approximation Theory, 16, 384-408 (1976) · Zbl 0322.41014
[6] Kammler, D. W., Chebyshev approximation of completely monotonie functions by sums of exponentials, SIAM J. Numer. Anal., 13, 761-774 (1976) · Zbl 0333.41016
[7] Karlin, S., Total Positivity (1968), Stanford Univ. Press: Stanford Univ. Press Stanford, Calif · Zbl 0219.47030
[8] Lanczos, C., Applied Analysis (1956), Prentice-Hall: Prentice-Hall Englewood Cliffs, N. J · Zbl 0111.12403
[9] Meinardus, C., Approximation of Functions: Theory and Numerical Methods, (Springer Tracts in Natural Philosophy, Vol. 13 (1967), Springer-Verlag: Springer-Verlag New York) · Zbl 0152.15202
[10] Natanson, I. P., Uniform Approximation, (Constructive Function Theory, Vol. 1 (1964), Ungar: Ungar New York) · Zbl 0133.31101
[11] De Prony, R., Essai expérimentale et analytique, J. Écol. Polytech. (Paris), 1, 24-76 (1795)
[12] Widder, D. V., The Laplace Transform (1941), Princeton Univ. Press: Princeton Univ. Press Princeton, N. J · Zbl 0060.24801
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