It is shown that no stable procedure for approximating functions from equally spaced
samples can converge exponentially for analytic functions. To avoid instability, one must …

This book uses asymptotic methods to obtain simple approximate analytic solutions to
various problems within mechanics, notably wave processes in heterogeneous materials …

The classical Gibbs phenomenon exhibited by global Fourier projections and interpolants
can be resolved in smooth regions by reprojecting in a truncated Gegenbauer series …

It is well known that the expansion of an analytic nonperiodic function on a finite interval in a
Fourier series leads to spurious oscillations at the interval boundaries. This result is known …

Let f(z) be an analytic or meromorphic function in the closed unit disk sampled at the n th
roots of unity. Based on these data, how can we approximately evaluate f(z) or f^(m)(z) at a …

We propose a novel pilot-aided algorithm for estimation of rapidly varying wireless channels
in OFDM systems. Our approach is specifically designed for channels varying on the scale of …

Uses the FPT to Solve the Quantification Problem in MRSAn invaluable tool in non-invasive
clinical oncology diagnosticsAddressing the critical need in clinical oncology for robust and …

We introduce a simple and efficient method to reconstruct an element of a Hilbert space in
terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a …

In this paper we consider several nonlinear systems of algebraic equations which can be
called “Prony-type.” These systems arise in various reconstruction problems in several …

In this paper, we give a constructive proof that a real, piecewise continuous function can be
almost uniformly approximated by single hidden-layer feedforward neural networks …