doi:10.3850/978-981-08-5118-7_045

ABSTRACT

A verified automatic integration algorithm is proposed for calculating contour integration over complex field using numerical computations. The proposed algorithm is based on trapezoidal rule for angle. The error analysis of the method have been presented by several authors, however, these investigations are done basically for examining the rates of convergence, and several constants in these error formula were left unevaluated. In order to construct verified numerical integrator using the algorithm, the error formula is presented. To construct efficient verified numerical integrator, an efficient a priori method of evaluating function calculation errors is adopted. Combining these, a verified automatic integration algorithm is proposed. Numerical examples are presented for illustrating effectiveness of the proposed algorithm.

Keywords: Numerical integration, Verification, Contour integraion.

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