Fourier Transform and Other Quadratic Problems under Interval Uncertainty

Authors

Oscar Galindo, The University of Texas at El PasoFollow
Christopher Ibarra, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

11-1-2021

Comments

Technical Report: UTEP-CS-21-96

Abstract

In general, computing the range of a quadratic function on given intervals is NP-hard. Recently, a feasible algorithm was proposed for computing the range of a specific quadratic function -- square of the modulus of a Fourier coefficient. For this function, the rank of the quadratic form -- i.e., the number of nonzero eigenvalues -- is 2. In this paper, we show that this algorithm can be extended to all the cases when the rank of the quadratic form is bounded by a constant.