Automatic, guaranteed integration of analytic functions
Combining the method to compute the bounds for homogeneous functional L on the set of analytic functions, which was developed by \textit{P. Davis} [J. Rat. Mech. Analysis 2, 303-313 (1953; Zbl 0050.130)], and ideas on using interval arithmetic, in particular the arithmetic operations on the set of complex circles, the author gives rigorous error bounds for numerical integration of analytic functions. After this, he develops a strategy to integrate numerically these functions. The strategy consists of the way how the interval of integration must be broken up into subintervals and then choosing the order of numerical integration formula used over each subinterval. Interval analysis and the aforementioned estimates are used to propose a program of automatic integration of analytic function with guaranteed accurracy. There are a discussion of the program, its possibilities, and three numerical examples.
numerical integration of analytic functions
scientific article; zbMATH DE number 4128289