Related papers: Fast Toeplitz eigenvalue computations, joining int…
This paper proposes a unique optimization approach for estimating the minimax rational approximation and its application for evaluating matrix functions. Our method enables the extension to generalized rational approximations and has the…
At variance with fully inclusive quantities, which have been computed already at the two- or three-loop level, most exclusive observables are still known only at one-loop, as further progress was hampered so far by the greater computational…
Closed-loop learning is the process of repeatedly estimating a model from data generated from the model itself. It is receiving great attention due to the possibility that large neural network models may, in the future, be primarily trained…
Many standard conversion matrices between coefficients in classical orthogonal polynomial expansions can be decomposed using diagonally-scaled Hadamard products involving Toeplitz and Hankel matrices. This allows us to derive…
Frank-Wolfe methods (FW) have gained significant interest in the machine learning community due to its ability to efficiently solve large problems that admit a sparse structure (e.g. sparse vectors and low-rank matrices). However the…
For some kernel matrices, low-rank approximations can be quickly obtained via analytic techniques. One important class of analytic methods that has received attention in recent years is based on the use of proxy points. Accuracy analysis…
Let $A$ be an infinite Toeplitz matrix with a real symbol $f$ defined on $[-\pi, \pi]$. It is well known that the sequence of spectra of finite truncations $A_N$ of $A$ converges to the convex hull of the range of $f$. Recently, Levitin and…
Recent hardware-aware matrix-free algorithms for higher-order finite-element (FE) discretized matrix-vector multiplications reduce floating point operations and data access costs compared to traditional sparse matrix approaches. This work…
By application of the theory for second-order linear differential equations with two turning points developed in [Olver F.W.J., Philos. Trans. Roy. Soc. London Ser. A 278 (1975), 137-174], uniform asymptotic approximations are obtained in…
In this article we present an emulation strategy for one-loop matrix elements. This strategy is based on the factorisation properties of matrix elements and is an extension of the work presented in arXiv:2107.06625. We show that a…
A Quasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind $A=T(a)+E$ where $T(a)=(a_{j-i})_{i,j\in\mathbb Z^+}$, $E=(e_{i,j})_{i,j\in\mathbb Z^+}$ is compact and the norms $\lVert a\rVert_{\mathcal W} = \sum_{i\in\mathbb Z}|a_i|$…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast…
Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning. In theory, under certain conditions, this problem can be…
The Frank Wolfe algorithm (FW) is a popular projection-free alternative for solving large-scale constrained optimization problems. However, the FW algorithm suffers from a sublinear convergence rate when minimizing a smooth convex function…
We study the spectrum of the Toeplitz matrix with a sine kernel, which corresponds to the single-particle reduced density matrix for free fermions on the one-dimensional lattice. For the spectral determinant of this matrix, a…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some of the output variables are also input variables, linked by a linear dependency. Fundamental examples…
In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional…
The Frank-Wolfe method has become increasingly useful in statistical and machine learning applications, due to the structure-inducing properties of the iterates, and especially in settings where linear minimization over the feasible set is…
We describe a method for the rapid numerical evaluation of the Bessel functions of the first and second kinds of nonnegative real orders and positive arguments. Our algorithm makes use of the well-known observation that although the Bessel…