On the convergence of product formulas for the evaluation of certain two-dimensional Cauchy principal value integrals

Author:
Giuseppe Mastroianni

Journal:
Math. Comp. **52** (1989), 95-101

MSC:
Primary 65D32; Secondary 41A55

MathSciNet review:
971404

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Abstract: The convergence of product rules of interpolatory type for the numerical evaluation of certain two-dimensional Cauchy principal value integrals is proved. Some estimates of the remainder are established for several classes of functions. Earlier results are generalized and improved.

**[1]**Giuliana Criscuolo and Giuseppe Mastroianni,*On the convergence of an interpolatory product rule for evaluating Cauchy principal value integrals*, Math. Comp.**48**(1987), no. 178, 725–735. MR**878702**, 10.1090/S0025-5718-1987-0878702-4**[2]**Giuliana Criscuolo and Giuseppe Mastroianni,*Convergence of Gauss type product formulas for the evaluation of two-dimensional Cauchy principal value integrals*, BIT**27**(1987), no. 1, 72–84. MR**874862**, 10.1007/BF01937356**[3]**C. Dagnino and A. Palamara Orsi,*On the evaluation of certain two-dimensional singular integrals with Cauchy kernels*, Numer. Math.**46**(1985), no. 1, 121–130. MR**777828**, 10.1007/BF01400259**[4]**Giovanni Monegato,*Convergence of product formulas for the numerical evaluation of certain two-dimensional Cauchy principal value integrals*, Numer. Math.**43**(1984), no. 2, 161–173. MR**736078**, 10.1007/BF01390121**[5]**Paul G. Nevai,*Orthogonal polynomials*, Mem. Amer. Math. Soc.**18**(1979), no. 213, v+185. MR**519926**, 10.1090/memo/0213**[6]**M. A. Šeško,*Convergence of cubature processes for a two-dimensional singular integral*, Dokl. Akad. Nauk BSSR**23**(1979), no. 4, 293–297, 380 (Russian, with English summary). MR**535655**

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DOI:
https://doi.org/10.1090/S0025-5718-1989-0971404-7

Article copyright:
© Copyright 1989
American Mathematical Society