Related papers: Efficient inverse $Z$-transform and Wiener-Hopf fa…
We prove simple general formulas for expectations of functions of a random walk and its running extremum. Under additional conditions, we derive analytical formulas using the inverse $Z$-transform, the Fourier/Laplace inversion and…
This paper introduces a new method for constructing approximate solutions to a class of Wiener--Hopf equations. This is particularly useful since exact solutions of this class of Wiener--Hopf equations, at the moment, cannot be obtained.…
We consider matrix functions with certain invariance under inversion in the unit circle. If such a function satisfies a positivity assumption on the unit circle, then only zero partial indices appear in its Riemann-Hilbert (Wiener-Hopf)…
As in the paper [G. Groenewald, M.A. Kaashoek, A.C.M. Ran, Wiener-Hopf indices of unitary functions on the unit circle in terms of realizations and related results on Toeplitz operators. \emph{Indag. Math.} 28 (2017) 694--710] our aim is to…
The paper is concerned with efficient numerical methods for solving a linear system $\phi(A) x= b$, where $\phi(z)$ is a $\phi$-function and $A\in \mathbb R^{N\times N}$. In particular in this work we are interested in the computation of…
We derive the L\'evy-Khintchine representation of the Wiener-Hopf factors for the Normal Inverse Gaussian (NIG) process as well as a representation which is similar to the moment generating function (MGF) of a generalized gamma convolution…
In some of the problems, complicated functions of the Z-transform variable, $z$, appear which either cannot be inverted analytically or the required calculations are quite tedious. In such cases numerical methods should be used to find the…
We establish left and right canonical factorizations of Hilbert-space operator-valued functions G(z) that are analytic on neighborhoods of the complex unit circle and the origin 0, and that have the form G(z)=I+F(z) with F(z) taking…
Embedding formula allows to recycle solution of a family boundary value problems by expressing all the solutions in terms of a small number of solutions. Such formulas have been previously derived in the context of diffraction by applying a…
The diffraction of a time-harmonic plane wave on collinear finite defects in a square lattice is studied. This problem is reduced to a matrix Wiener-Hopf equation. This work adapts the recently developed iterative Wiener-Hopf method to this…
In this paper we propose a method for computing the Faddeeva function $w(z) := e^{-z^2}\mathrm{erfc}(-i z)$ via truncated modified trapezoidal rule approximations to integrals on the real line. Our starting point is the method due to Matta…
We propose a hyperpower iteration for numerical computation of the outer generalized inverse of a matrix which achieves the 18th order of convergence by using only seven matrix multiplication per iteration loop. This is the record high…
In the work we propose an algorithm for a Wiener -- Hopf factorization of scalar polynomials based on notions of indices and essential polynomials. The algorithm uses computations with finite Toeplitz matrices and permits to obtain…
We present a fast Gauss transform in one dimension using nearly optimal sum-of-exponentials approximations of the Gaussian kernel. For up to about ten-digit accuracy, the approximations are obtained via best rational approximations of the…
We give a self-contained randomized algorithm based on shifted inverse iteration which provably computes the eigenvalues of an arbitrary matrix $M\in\mathbb{C}^{n\times n}$ up to backward error $\delta\|M\|$ in…
In recent years, a new kind of accelerated hardware has gained popularity in the Artificial Intelligence (AI) and Machine Learning (ML) communities which enables extremely high-performance tensor contractions in reduced precision for deep…
We develop embedding formulae for all possible diffraction problems with Dirichlet scatterers on square lattices using the Wiener--Hopf perspective. The embedding formula expresses solutions for arbitrary plane-wave incidence in terms of a…
We present a MATLAB function for the numerical evaluation of the Faddeyeva function w(z). The function is based on a newly developed accurate algorithm. In addition to its higher accuracy, the software provides a flexible accuracy vs…
Matrix operations such as matrix inversion, eigenvalue decomposition, singular value decomposition are ubiquitous in real-world applications. Unfortunately, many of these matrix operations so time and memory expensive that they are…
We present numerical methods based on the fast Fourier transform (FFT) to solve convolution integral equations on a semi-infinite interval (Wiener-Hopf equation) or on a finite interval (Fredholm equation). We extend and improve a FFT-based…