Functions of one or more variables are usually approximated with a basis: a complete,
linearly independent system of functions that spans a suitable function space. The topic of …

We propose AAA rational approximation as a method for interpolating or approximating
smooth functions from equispaced samples. Although it is always better to approximate from …

An effective means to approximate an analytic, nonperiodic function on a bounded interval is
by using a Fourier series on a larger domain. When constructed appropriately, this so-called …

In a previous paper (Adcock and Huybrechs in SIAM Rev 61 (3): 443–473, 2019) we
described the numerical approximation of functions using redundant sets and frames …

Abstract We present a Fourier Continuation-based parallel pseudospectral method for
incompressible fluids in cuboid non-periodic domains. The method produces dispersionless …

Fourier series of smooth, nonperiodic functions on -1,1 are known to exhibit the Gibbs
phenomenon, and they exhibit overall slow convergence. One way of overcoming these …

Due to growing demands on newly developed products concerning their weight, sound
emission, etc., advanced materials are introduced in the product designs. The modeling of …

Functions that are smooth but non-periodic on a certain interval possess Fourier series that
lack uniform convergence and suffer from the Gibbs phenomenon. However, they can be …

We introduce an algorithm for the least squares solution of a rectangular linear system Ax=b,
in which A may be arbitrarily ill-conditioned. We assume that a complementary matrix Z is …

Fourier extension is an approximation scheme in which a function on an arbitrary bounded
domain is approximated using classical Fourier series on a bounding box. On the domain of …