Philip Rabinowitz – Communications of the ACM

Research and Advances May 1 1969

Rough and ready error estimates in Gaussian integration of analytic functions

Two expressions are derived for use in estimating the error in the numerical integration of analytic functions in terms of the maximum absolute value of the function in an appropriate region of regularity. These expressions are then specialized to the case of Gaussian integration rules, and the resulting error estimates are compared with those obtained by the use of tables of error coefficients.

Systems and Networking

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Research and Advances Nov 1 1968

Practical error coefficients in the integration of periodic analytic functions by the trapezoidal rule

Theoretical and practical values of error coefficients useful in bounding the error in integrating periodic analytic functions with the trapezoidal rule are tabulated for various ranges of the parameters.

Research and Advances Jan 1 1968

Numerical Analysis: Practical error coefficients for estimating quadrature errors for analytic functions

Research and Advances Nov 1 1966

Automatic integration of a function with a parameter

Two efficient methods for automatic numerical integration are Romberg integration and adaptive Simpson integration. For integrands of the form ƒ(x)g(x, &agr;) where &agr; is a parameter, it is shown that Romberg's method is more efficient. A FORTRAN program shows how to achieve this greater efficiency.

Research and Advances Feb 1 1961

Multiple-precision division

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