| Title:
|
Mean square approximation by optimal periodic interpolation (English) |
| Author:
|
Delvos, Franz-J. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
40 |
| Issue:
|
4 |
| Year:
|
1995 |
| Pages:
|
267-283 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Following the research of Babuška and Práger, the author studies the approximation power of periodic interpolation in the mean square norm thus extending his own former results. (English) |
| Keyword:
|
mean square approximation |
| Keyword:
|
periodic Hilbert space |
| Keyword:
|
exponential interpolants |
| Keyword:
|
optimal periodic interpolation |
| MSC:
|
41A05 |
| MSC:
|
65D05 |
| idZBL:
|
Zbl 0836.41002 |
| idMR:
|
MR1331918 |
| DOI:
|
10.21136/AM.1995.134294 |
| . |
| Date available:
|
2009-09-22T17:48:15Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134294 |
| . |
| Reference:
|
[1] I. Babuška: Über universal optimale Quadraturformeln. Teil 1.Apl. mat. 13 (1968), 304–308. MR 0244680 |
| Reference:
|
[2] E.W. Cheney: Approximation by functions of nonclassical form.Approximation theory, Spline functions and Applications, S.P. Singh (ed.), NATO ASI Series C, 356, 1992, pp. 1–18. Zbl 0751.41001, MR 1165960 |
| Reference:
|
[3] F.-J. Delvos: Periodic interpolation on uniform meshes.J. Approximation Theory 51 (1987), 71–80. Zbl 0664.41004, MR 0906762, 10.1016/0021-9045(87)90096-7 |
| Reference:
|
[4] F.-J. Delvos: Approximation by optimal periodic interpolation.Apl. mat. 35 (1990), 451–457. Zbl 0743.41005, MR 1089925 |
| Reference:
|
[5] S.L. Lee, W.S. Tang: Approximation and spectral properties of periodic spline operators.Proc. Edinburgh Math. Soc. 34 (1991), 363–382. MR 1131957 |
| Reference:
|
[6] S.L. Lee, R.C.E. Tan, W.S. Tang: $L_2$-approximation by the translates of a function and related attenuation factors..Numer. Math. 60 (1992), 549–568. MR 1142312, 10.1007/BF01385736 |
| Reference:
|
[7] F. Locher: Interpolation on uniform meshes by the translates of the function and related attenuation factors.Math. Comput. 37 (1981), 403–416. MR 0628704, 10.1090/S0025-5718-1981-0628704-2 |
| Reference:
|
[8] M. Práger: Universally optimal approximation of functionals.Apl. mat. 24 (1979), 406–420. MR 0547044 |
| . |
