In recent works, the authors introduced a neural operator: a special type of neural networks
that can approximate maps between infinite-dimensional spaces. Using numerical and …

Recent advances in high-resolution imaging techniques and particle-based simulation
methods have enabled the precise microscopic characterization of collective dynamics in …

We review recent advances in algorithms for quadrature, transforms, differential equations
and singular integral equations using orthogonal polynomials. Quadrature based on …

We are given one input–output (io) trajectory (u, y) produced by a linear, continuous time-
invariant system, and we compute its Chebyshev polynomial series representation. We …

What if all you had to do to solve an ODE were just to write it down? 1 That is the line we will
follow in this book. Our emphasis is not just on the mathematics of ODEs, but on how the …

We extend the ultraspherical spectral method to solving nonlinear ordinary differential
equation (ODE) boundary value problems. Naive ultraspherical Newton implementations …

We consider two main inverse Sturm–Liouville problems: the problem of recovery of the
potential and the boundary conditions from two spectra or from a spectral density function. A …

Analytic continuation is ill-posed, but becomes merely ill-conditioned (although with an
infinite condition number) if it is known that the function in question is bounded in a given …

This work is concerned with approximating a trivariate function defined on a tensor-product
domain via function evaluations. Combining tensorized Chebyshev interpolation with a …

We propose a continuous approach for computing the pseudospectra of linear operators
following a'solve-then-discretize'strategy. Instead of taking a finite section approach or using …