Abstract
A summary is given of Philip Rabinowitz's contributions to numerical analysis with emphasis on his work on integration.
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References
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P.C. Hammer and A.H. Stroud, Numerical evaluation of multiple integrals. II, Math. Tables Aids Comp. 12 (1958) 272–280.
A.S. Kronrod,Nodes and Weights for Quadrature Formulae. Sixteen-place Tables (Russian) (Izdat. “Nauka”, Moscow, 1964). [English transl.: Consultants Bureau, New York, 1965.]
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D.S. Lubinsky and P. Rabinowitz, Rates of convergence of Gaussian quadrature for singular integrands, Math. Comp. 43 (1984) 219–242.
D.S. Lubinsky and P. Rabinowitz, Hermite and Hermite-Fejér interpolation and associated product integration rules on the real line: TheL 1 theory, Canad. J. Math. 44 (1992) 561–590.
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P. Rabinowitz, Convergence results for piecewise linear quadratures for Cauchy principal value integrals, Math. Comp. 51 (1988) 741–747.
P. Rabinowitz, Product integration based on Hermite-Fejér interpolation, J. Comp. Appl. Math. 28 (1989) 85–101.
P. Rabinowitz, On an interpolatory product rule for evaluating Cauchy principal value integrals, BIT 29 (1989) 347–355.
P. Rabinowitz, Numerical integration based on approximating splines, J. Comp. Appl. Math. 33 (1990) 73–83.
P. Rabinowitz, Numerical evaluation of Cauchy principal value integrals with singular integrands, Math. Comp. 55 (1990) 265–276.
P. Rabinowitz, Generalized noninterpolatory rules for Cauchy principal value integrals, Math. Comp. 54 (1990) 217–279.
P. Rabinowitz, Uniform convergence of Cauchy principal value integrals of interpolating splines, Israel Math. Conf. Proc. 4 (1991) 225–231.
P. Rabinowitz, Extrapolation methods in numerical integration, Numer. Algor. 3 (1992) 17–28.
P. Rabinowitz, S. Elhay and J. Kautsky, Empirical mathematics: the first Patterson extension of Gauss-Kronrod rules, Int. J. Comp. Math. 36 (1990) 119–129.
P. Rabinowitz and L. Gori,L 1-norm convergence of Hermite-Fejér interpolation based on the Laguerre and Hermite abscissas, Rend. Mat. Appl. (7) 14 (1994) 159–176.
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P. Rabinowitz and W.E. Smith, Interpolatory product integration for Riemann-integrable functions, J. Austral. Math. Soc. Ser. B 29 (1987) 195–202.
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Gautschi, W. The work of Philip Rabinowitz on numerical integration. Numer Algor 9, 199–222 (1995). https://doi.org/10.1007/BF02141588
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DOI: https://doi.org/10.1007/BF02141588