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On approximation of functions by exponential sums. (English) Zbl 1075.65022
Similar to the well-known Fourier expansions and approximations, approximations by finite sums of exponentials with complex exponents are studied in this article. Associated with such approximations are Hankel matrices which come from the selection of exponentials as basis functions for the approximation. It is shown that the errors of the aforementioned approximations can be found by computing singular values of certain (finite) Hankel matrices. Algorithms for the computations of the approximations are given, as well as many examples to show the usefulness of the new approach.

MSC:
65D15 Algorithms for approximation of functions
11L03 Trigonometric and exponential sums, general
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