| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| DOI:
|
10.21136/AM.1973.103467 |
| . |
| Date available:
|
2008-05-20T17:56:04Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103467 |
| . |
| 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. |
| . |
