Convergence results for piecewise linear quadratures for Cauchy principal value integrals
Author:
Philip Rabinowitz
Journal:
Math. Comp. 51 (1988), 741747
MSC:
Primary 65D30; Secondary 41A55
MathSciNet review:
958639
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Abstract: Conditions on k and f are given for the pointwise and uniform convergence to the Cauchy principal value integral of a sequence of integrals of piecewise linear approximations to or . The important special case, , is considered in detail.
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 [1]
 G. Criscuolo & G. Mastroianni, "On the convergence of an interpolatory product rule for evaluating Cauchy principal value integrals," Math. Comp., v. 48, 1987, pp. 725735. MR 878702 (88m:65038)
 [2]
 A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Tables of Integral Transforms, vol. II, McGrawHill, New York, 1954. MR 0065685 (16:468c)
 [3]
 A. Gerasoulis, "Piecewisepolynomial quadratures for Cauchy singular integrals," SIAM J. Numer. Anal., v. 23, 1986, pp. 891902. MR 849289 (87m:65039)
 [4]
 P. Rabinowitz, "Numerical integration in the presence of an interior singularity," J. Comput. Appl. Math., v. 17, 1987, pp. 3141. MR 884259 (88e:65022)
 [5]
 P. Rabinowitz, "The convergence of noninterpolatory product integration rules," in Numerical Integration (P. Keast and G. Fairweather, eds.), Reidel, Dordrecht, 1987, pp. 116. MR 907108 (88i:65044)
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 C. Stewart, "On the numerical evaluation of singular integrals of Cauchy type," J. Soc. Indust. Appl. Math., v. 8, 1960, pp. 342353. MR 0114101 (22:4928)
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 G. Szegö, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R.I., 1975.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198809586393
PII:
S 00255718(1988)09586393
Keywords:
Cauchy principal value integrals,
piecewise linear approximation,
product integration,
Jacobi weight function
Article copyright:
© Copyright 1988
American Mathematical Society
