| Title:
|
Recurrent evaluation of integrals of the type $\int^1_0x^\alpha\sin 2\pi px dx$, $\int^1_0x^\alpha\cos 2\pi px dx$ with respect to numerical stability (English) |
| Author:
|
Chvála, František |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
20 |
| Issue:
|
3 |
| Year:
|
1975 |
| Pages:
|
206-215 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with recurrent processes for the evalutaion of integrals occurring in the numerical Fourier analysis. The problem of preventing a substantial influence of round-off errors accumulation is discussed and a numerically stable algorithm is developed. The theory is supplied with illustrative numerical examples. () |
| MSC:
|
41A55 |
| MSC:
|
65D20 |
| MSC:
|
65D30 |
| MSC:
|
65T05 |
| idZBL:
|
Zbl 0307.65033 |
| idMR:
|
MR0371129 |
| DOI:
|
10.21136/AM.1975.103584 |
| . |
| Date available:
|
2008-05-20T18:01:16Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103584 |
| . |
| Reference:
|
[1] Mikloško J.: Numerical integration with weight functions cos kx, sin kx on $[0, 2 \pi /t]$, t = = 1, 2, ....Apl. mat. 14 (1969), 179-194. MR 0246510 |
| Reference:
|
[2] Крылов В. И.: Приближенное вычисление интегралов.Наука, Москва 1967, гл. 14. Zbl 1103.35360 |
| Reference:
|
[3] Babušková R.: Über numerische Stabilität einiger Rekursionsformeln.Apl. mat. 9 (1964), 186-193. MR 0187365 |
| Reference:
|
[4] Babuška I., Práger M., Vitásek E.: Numerical processes in differential equations.Wiley, London-New York-Sydney 1966, chap. 2. MR 0223101 |
| Reference:
|
[5] Fleckner O. L.: A method for the computation of the Fresnel integrals and related functions.Math. Соmр. 22 (1968), 635-640. Zbl 0159.45201, MR 0226824 |
| Reference:
|
[6] Bulirsch R., Stoer J.: Numerical treatment of ordinary differential equations by extrapolation methods.Numer. Math. 8 (1966), 1 - 13. Zbl 0135.37901, MR 0191095, 10.1007/BF02165234 |
| Reference:
|
[7] Chvála F.: Evaluation of integrals by means of recurrence formulae.Report ÚVT ČVUT 2/73 (in czech). |
| . |
