We introduce a new approach, and associated algorithms, for the efficient approximation of
functions and sequences by short linear combinations of exponential functions with complex-…

We revisit the efficient approximation of functions by sums of exponentials or Gaussians in
Beylkin and Monzón (2005) [16] to discuss several new results and applications of these …

These new quadratures can be used to approximate and integrate bandlimited functions,
such as prolate spheroidal wave functions, and essentially bandlimited functions, such as …

New compactly supported wavelets for which both the scaling and wavelet functions have a
high number of vanishing moments are presented. Such wavelets are a generalization of the …

This paper presents an extension of the Adaptive Antoulas–Anderson (AAA) algorithm for
rational modeling. Specifically, our new stable multi-input multi-output AAA (smiAAA) algorithm …

We construct an approximation of the free space Green’s function for the Helmholtz equation
that splits the application of this operator between the spatial and the Fourier domains, as in …

We consider the problem of reconstructing a compactly supported function with singularities
either from values of its Fourier transform available only in a bounded interval or from a …

The formal representation of the quasi-periodic Helmholtz Green's function obtained by the
method of images is only conditionally convergent and, thus, requires an appropriate …

Protection systems are a critical feature for the proper operation of a power grid. Protection
systems should be able to quickly detect, identify, locate, and isolate the faults within a time …

Modern computers have made commonplace many calculations that were impossible to
imagine a few years ago. Still, when you face a problem with a high physical dimension, you …