On some applications of circular complex functions (Q1115091)

Some possibilities for the application of the arithmetic of disks (circular arithmetic) in solving problems concerning complex integration are presented. In section 2 a short review of some properties of the arithmetic of disks is considered; in section 3, the problem of computing a curvilinear integral in the presence of a round-off error and uncertain initial data is studied; in section 4 an error estimate for the numerical integration of interpolatory type along a circle is given and in section 5 an estimation of the remainder of Taylor's series is obtained.