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We study one-dimensional integral inequalities, with quadratic integrands, on bounded domains. Conditions for these inequalities to hold are formulated in terms of function matrix inequalities which must hold in the domain of integration.…
The iterative method of Sinkhorn allows, starting from an arbitrary real matrix with non-negative entries, to find a so-called 'scaled matrix' which is doubly stochastic, i.e. a matrix with all entries in the interval (0, 1) and with all…
Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…
A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…
We devise achievable encoding schemes for distributed source compression for computing inner products, symmetric matrix products, and more generally, square matrix products, which are a class of nonlinear transformations. To that end, our…
This paper addresses the structure-and-motion problem, that requires to find camera motion and 3D struc- ture from point matches. A new pipeline, dubbed Samantha, is presented, that departs from the prevailing sequential paradigm and…
We analyze and develop numerical methods for time-harmonic wave scattering in metallic waveguide structures of infinite extent. We show that radiation boundary conditions formulated via projectors onto outgoing modes determine the…
Pseudospectral analysis serves as a powerful tool in matrix computation and the study of both linear and nonlinear dynamical systems. Among various numerical strategies, random sampling, especially in the form of rank-$1$ perturbations,…
We consider nonlinear delay differential and renewal equations with infinite delay. We extend the work of Gyllenberg et al, Appl. Math. Comput. (2018) by introducing a unifying abstract framework, and derive a finite-dimensional…
The problem of diagonalizing a class of complicated matrices, to be called ultrametric matrices, is investigated. These matrices appear at various stages in the description of disordered systems with many equilibrium phases by the technique…
The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give…
For solving the continuous Sylvester equation, a class of the multiplicative splitting iteration method is presented. We consider two symmetric positive definite splittings for each coefficient matrix of the continuous Sylvester equations…
The Eigendecomposition of quadratic forms (symmetric matrices) guaranteed by the spectral theorem is a foundational result in applied mathematics. Motivated by a shared structure found in inferential problems of recent interest---namely…
We develop a procedure for determining whether a square complex matrix is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. Our approach has several advantages over existing methods. We discuss these differences and…
We present an adaptation of the so-called structural method \cite{CMM23} for Hamiltonian systems, and redesign the method for this specific context, which involves two coupled differential systems. Structural schemes decompose the problem…
Matrix mechanisms are often used to provide unbiased differentially private query answers when publishing statistics or creating synthetic data. Recent work has developed matrix mechanisms, such as ResidualPlanner and Weighted Fourier…
Pseudo-hermitian matrices are matrices hermitian with respect to an indefinite metric. They can be thought of as the truncation of pseudo-hermitian operators, defined over some Krein space, together with the associated metric, to a finite…
The cyclotomic matrix is commonly used to arrange cyclotomic numbers in a convenient format. A natural question is whether the structure of the matrix can reflect properties of these numbers. In this article, we examine cyclotomic numbers…
The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…
Convergence properties of binary stationary subdivision schemes for curves have been analyzed using the techniques of z-transforms and eigenanalysis. Eigenanalysis provides a way to determine derivative continuity at specific points based…