An increasing complexity of practical problems requires a comparative analysis of the accuracy and effectiveness of optimal methods (and methods close to optimal with respect to their computational characteristics) that exist for the solution of problems in applied and computational mathematics. In many cases we need improvements in methods for the estimation of computational errors. This paper addresses these issues for the optimisation of the accuracy of the numerical evaluation of certain oscillatory integrals. Such integrals occur as an important part of the modelling of optical systems and automatic control systems. They also occur in digital filtering, image recognition, statistical analysis of experimental data and many other problems [2, 4]. The algorithms described in this paper are designed to solve some practical problems in digital signal processing and image recognition. They deal with the case of inaccurate data and provide estimates of accuracy in the solutions.
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