| Title:
|
On a new kind of 2-periodic trigonometric interpolation (English) |
| Author:
|
Jiang, Tianzi |
| Author:
|
Ma, Songde |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
41 |
| Issue:
|
6 |
| Year:
|
1996 |
| Pages:
|
401-410 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is well-known that the interpolation theory plays an important role in many fields of computer vision, especially in surface reconstruction. In this paper, we introduce a new kind of 2-period interpolation of functions with period $2\pi $. We find out the necessary and sufficient conditions for regularity of this new interpolation problem. Moreover, a closed form expression for the interpolation polynomial is given. Our interpolation is of practical significance. Our results provide the theoretical basis for using our interpolation in practical problems. (English) |
| Keyword:
|
Interpolation |
| Keyword:
|
trigonometric polynomial |
| Keyword:
|
regularity |
| Keyword:
|
computer vision |
| MSC:
|
41A05 |
| MSC:
|
42A15 |
| idZBL:
|
Zbl 0870.41002 |
| idMR:
|
MR1415248 |
| DOI:
|
10.21136/AM.1996.134334 |
| . |
| Date available:
|
2009-09-22T17:52:32Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134334 |
| . |
| Reference:
|
[s1] G.G. Lorentz, K. Jetter and S.D. Riemenschneider: Birkhoff Interpolation.Addison-Wesley Publishing Co., Reading, Mass., 1983. MR 0680938 |
| Reference:
|
[s2] A. Sharmea, J. Szabados and R.S. Varga: 2-periodic lacunary trigonometric interpolation: $(0,M)$ case.Proc. Conf. on Constructive Theory of Functions’87, Varna, Bulgaria, pp. 420–426. |
| Reference:
|
[s3] A. Sharmea, Sun Xiehua: A 2-periodic Trigonometric Interpolation Problem.Approx. Theory and its Appl. 8 (1992), no. 4, 1–16. MR 1212842 |
| Reference:
|
[s4] J. Szabados: On the Rate of Convergence of a Lacunary Trigonometric interpolation Process.Acta Math. Hungar. 47 (1986), 361–370. Zbl 0694.42006, MR 0854522, 10.1007/BF01953973 |
| Reference:
|
[s5] Liu Yongping: On the trigonometric interpolation and the entire interpolation.Approx. Theory and its Appl. 6 (1990), no. 4, 85–106. Zbl 0724.42005, MR 1106069 |
| . |
