| Title:
|
Further convergence results for two quadrature rules for Cauchy type principal value integrals (English) |
| Author:
|
Ioakimidis, Nikolaos I. |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
27 |
| Issue:
|
6 |
| Year:
|
1982 |
| Pages:
|
457-466 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
New convergence and rate-of-convergence results are established for two well-known quadrature rules for the numerical evaluation of Cauchy type principal value integrals along a finite interval, namely the Gauss quadrature rule and a similar interpolatory quadrature rule where the same nodes as in the Gauss rule are used. The main result concerns the convergence of the interpolatory rule for functions satisfying the Hölder condition with exponent less or equal to $\frac12$. The results obtained here supplement a series of previous results on the convergence of the aforementioned quadrature rules. (English) |
| Keyword:
|
rate-of-convergence |
| Keyword:
|
quadrature rules |
| Keyword:
|
Cauchy type principal value integrals |
| Keyword:
|
finite interval |
| Keyword:
|
Gauss quadrature |
| Keyword:
|
interpolatory quadrature |
| MSC:
|
30E20 |
| MSC:
|
65D05 |
| MSC:
|
65D30 |
| MSC:
|
65D32 |
| idZBL:
|
Zbl 0518.65009 |
| idMR:
|
MR0678115 |
| DOI:
|
10.21136/AM.1982.103992 |
| . |
| Date available:
|
2008-05-20T18:20:37Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103992 |
| . |
| Reference:
|
[1] E. W. Cheney: Introduction to Approximation Theory.McGraw-Hill, New York, 1966. Zbl 0161.25202, MR 0222517 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[7] D. B. Hunter: Some Gauss-Type Formulae for the Evaluation of Cauchy Principal Values of Integrals.Numerische Mathematik, 1972, Vol. 19, pp. 419-424. Zbl 0231.65028, MR 0319355, 10.1007/BF01404924 |
| Reference:
|
[8] N. I. Ioakimidis: General Methods for the Solution of Crack Problems in the Theory of Plane Elasticity.Doctoral Thesis at the National Technical University of Athens, Athens, 1976. [Available from University Microfilms, Ann Arbor, Michigan; Order No. 76-21, 056.] Zbl 0351.73109, MR 0521392 |
| Reference:
|
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| Reference:
|
[10] A. I. Kalandiya: Mathematical Methods of Two-dimensional Elasticity.1st English ed. Mir Publishers, Moscow, 1975. MR 0400846 |
| Reference:
|
[11] A. A. Korneichuk: Quadrature Formulae for Singular Integrals.In: Numerical Methods for the Solution of Differential and Integral Equations and Quadrature Formulae, Moscow, Nauka, 1964, pp. 64-74 (in Russian). |
| Reference:
|
[12] D. F. Paget, D. Elliott: An Algorithm for the Numerical Evaluation of Certain Cauchy Principal Value Integrals.Numerische Mathematik, 1972, Vol. 19, pp. 373 - 385. Zbl 0229.65091, MR 0366004, 10.1007/BF01404920 |
| Reference:
|
[13] T. J. Rivlin: An Introduction to the Approximation of Functions.1st ed. Blaisdell, Waltham, Massachusetts, 1969. Zbl 0189.06601, MR 0249885 |
| Reference:
|
[14] D. G. Sanikidze: On a Uniform Estimation of Approximation of Singular Integrals with Chebyshev's Weight Function by Sums of Interpolating Type.Soobščenija Akademii Nauk Gruzinskoī SSR, 1974, Vol. 75 (No. 1), pp. 53-55 (in Russian). MR 0358242 |
| Reference:
|
[15] M. A. Sheshko: On the Convergence of Quadrature Processes for a Singular Integral.Soviet Mathematics (Izvestija Vysših Učebnyh Zavedeniī. Matematika), 1976, Vol. 20 (No. 12), pp. 86-94. |
| Reference:
|
[16] G. Szegö: Orthogonal Polynomials.revised ed. American Mathematical Society, New York, 1959. MR 0106295 |
| Reference:
|
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| . |
