Related papers: A sparse spectral method for Volterra integral equ…

We study classical solutions (existence, uniqueness, and explicit solution operator) for homogeneous, linear, and semilinear abstract Volterra integral equations of wave type with almost sectorial operators. We use a functional calculus for…

We introduce a method which provides accurate numerical solutions to fractional-in-time partial differential equations posed on $[0,T] \times \Omega$ with $\Omega \subset \mathbb{R}^d$ without the excessive memory requirements associated…

The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a…

Sparse inducing points have long been a standard method to fit Gaussian processes to big data. In the last few years, spectral methods that exploit approximations of the covariance kernel have shown to be competitive. In this work we…

We look for spectral type differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with…

The paper focuses on solving one class of Volterra equations of the first kind, which is characterized by the variability of all integration limits. These equations were introduced in connection with the problem of identifying nonsymmetric…

We present an overarching framework for stable spectral methods on a triangle, defined by a multivariate W-system and based on orthogonal polynomials on the triangle. Motivated by the Koornwinder orthogonal polynomials on the triangle, we…

The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the…

We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in contrast to the work [17], where the single vector signal can be…

This article presents a higher-order spectral element method for the two-dimensional Stokes interface problem involving a piecewise constant viscosity coefficient. The proposed numerical formulation is based on least-squares formulation.…

For a general third-order tensor $\mathcal{A}\in\mathbb{R}^{n\times n\times n}$ the paper studies two closely related problems, an SVD-like tensor decomposition and an (approximate) tensor diagonalization. We develop a Jacobi-type algorithm…

One of the biggest open problems in computational algebra is the design of efficient algorithms for Gr{\"o}bner basis computations that take into account the sparsity of the input polynomials. We can perform such computations in the case of…

We address a linear fractional differential equation and develop effective solution methods using algorithms for inversion of triangular Toeplitz matrices and the recently proposed QTT format. The inverses of such matrices can be computed…

Given a way to evaluate an unknown polynomial with integer coefficients, we present new algorithms to recover its nonzero coefficients and corresponding exponents. As an application, we adapt this interpolation algorithm to the problem of…

This paper describes a trapezoidal quadrature method for the discretization of weakly singular, singular and hypersingular boundary integral operators with complex symmetric quadratic forms. Such integral operators naturally arise when…

This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector…

We derive formulae for the calculation of Taylor coefficients of solutions to systems of Volterra integral equations, both linear and nonlinear, either without singularities or with singularities of Abel type and logarithmic type. We also…

In the paper stochastic Volterra equations of nonscalar type in Hilbert space are studied. The aim of the paper is to provide some results on stochastic convolution and mild solutions to those Volterra equations. The motivation of the paper…

This paper is concerned with the numerical solution for a class of nonlinear weakly singular Volterra integral equation of the first kind. The existence and uniqueness issue of the nonlinear Abel integral equations is studied completely. An…

This paper considers the hyperparameter optimization problem of mathematical techniques that arise in the numerical solution of differential and integral equations. The well-known approaches grid and random search, in a parallel algorithm…