# Further convergence results for two quadrature rules for Cauchy type principal value integrals

Aplikace matematiky (1982)

- Volume: 27, Issue: 6, page 457-466
- ISSN: 0862-7940

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topIoakimidis, Nikolaos I.. "Further convergence results for two quadrature rules for Cauchy type principal value integrals." Aplikace matematiky 27.6 (1982): 457-466. <http://eudml.org/doc/15266>.

@article{Ioakimidis1982,

abstract = {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 $\frac\{1\}\{2\}$. The results obtained here supplement a series of previous results on the convergence of the aforementioned quadrature rules.},

author = {Ioakimidis, Nikolaos I.},

journal = {Aplikace matematiky},

keywords = {rate-of-convergence; quadrature rules; Cauchy type principal value integrals; finite interval; Gauss quadrature; interpolatory quadrature; rate-of-convergence; quadrature rules; Cauchy type principal value integrals; finite interval; Gauss quadrature; interpolatory quadrature},

language = {eng},

number = {6},

pages = {457-466},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Further convergence results for two quadrature rules for Cauchy type principal value integrals},

url = {http://eudml.org/doc/15266},

volume = {27},

year = {1982},

}

TY - JOUR

AU - Ioakimidis, Nikolaos I.

TI - Further convergence results for two quadrature rules for Cauchy type principal value integrals

JO - Aplikace matematiky

PY - 1982

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 27

IS - 6

SP - 457

EP - 466

AB - 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 $\frac{1}{2}$. The results obtained here supplement a series of previous results on the convergence of the aforementioned quadrature rules.

LA - eng

KW - rate-of-convergence; quadrature rules; Cauchy type principal value integrals; finite interval; Gauss quadrature; interpolatory quadrature; rate-of-convergence; quadrature rules; Cauchy type principal value integrals; finite interval; Gauss quadrature; interpolatory quadrature

UR - http://eudml.org/doc/15266

ER -

## References

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