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TW 339
P. Kravanja, T. Sakurai, M. Van Barel
Error analysis of a derivative-free algorithm for computing zeros of analytic functions
Abstract
We consider the quadrature method developed by Kravanja and Van Barel (Computing 63(1):69--91, 1999) for computing all the zeros of an analytic function that lie inside the unit circle. The algorithm uses only the function values and no (first or higher order) derivatives. Information about the location of the zeros is obtained from certain integrals along the unit circle. In numerical computations these are replaced by their trapezoidal rule approximations. We investigate the resulting quadrature error. Our error analysis shows that it actually has no effect at all on the computed approximations for the zeros.
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