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Efficient representation and accurate evaluation of oscillatory integrals and functions

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  • We introduce a new method for functional representation of oscillatory integrals within any user-supplied accuracy. Our approach is based on robust methods for nonlinear approximation of functions via exponentials. The complexity of evaluation of the resulting representations of the oscillatory integrals does not depend or depends only mildly on the size of the parameter responsible for the oscillatory behavior.
    Mathematics Subject Classification: Primary: 65D15, 65D30; Secondary: 41A55.

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