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Title: An algorithm for Hermite-Birkhoff interpolation (English)
Author: Fiala, Jiří
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 18
Issue: 3
Year: 1973
Pages: 167-175
Summary lang: English
Summary lang: Czech
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Category: math
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Summary: An algorithm for the Hermite-Birkhoff interpolation is presented, which reduces the problem to the Hermite interpolation. The missing values and derivatives are expressed by some of the given values and calculated from a system of linear equations. The system itself and its right-hand sides are computed from a set of Hermite interpolation problems. The needed values and derivatives of the Hermite interpolation polynomial can be computed using the algorithm given in the Appendix. ()
MSC: 65D05
idZBL: Zbl 0264.65007
idMR: MR0324871
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Date available: 2008-05-20T17:56:04Z
Last updated: 2015-08-06
Stable URL: http://hdl.handle.net/10338.dmlcz/103467
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Reference: [1] I. J. Schoenberg: On Hermite-Birkhoff interpolation.J. Math. Anal. Appl. 16(1966) 538-543. Zbl 0156.28702, MR 0203307, 10.1016/0022-247X(66)90160-0
Reference: [2] J. Fiala: Interpolation with prescribed values of derivatives instead of function values.Apl. mat. 16 (1971) 421-430. Zbl 0224.65002, MR 0292261
Reference: [3] J. N. Lyness C. B. Moler: Van der Monde systems and numerical differentiation.Num. Math. 8 (1966) 458-464. MR 0201071, 10.1007/BF02166671
Reference: [4] G. Galimberti V. Pereyra: Solving confluent Vandermonde systems of Hermite type.Num. Math. 18 (1971) 44-60. MR 0300417, 10.1007/BF01398458
Reference: [5] S., Å. Gustafson: Rapid computation of general interpolation formulas and mechanical quadrature rules.CACM 14 (1971) 797-801. Zbl 0226.65012, MR 0311069, 10.1145/362919.362941
Reference: [6] S., Å. Gustafson: A416: Rapid computation of interpolation formulas.CACM 14 (1971) 806-807. MR 0311070, 10.1145/362919.362951
Reference: [7] I. S. Berezin N. P. Židkov: Methods of Computations I.(Russian). M 1959.
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