Toeplitz matrices are abundant in computational mathematics, and there is a rich literature on the development of fast and superfast algorithms for solving linear systems involving such matrices. Any Toeplitz matrix can be transformed into a matrix with of ...
The randomized singular value decomposition (SVD) has become a popular approach to computing cheap, yet accurate, low-rank approximations to matrices due to its efficiency and strong theoretical guarantees. Recent work by Boullé and Townsend [Found. Comput ...
Society for Industrial & Applied Mathematics (SIAM)2025
A result by Crouzeix and Palencia states that the spectral norm of a matrix function (Formula presented.) is bounded by (Formula presented.) times the maximum of f on (Formula presented.), the numerical range of A. The purpose of this work is to point out ...
Given a Hilbert space H and a finite measure space Ω, the approximation of a vector-valued function f:Ω→H by a k-dimensional subspace U⊂H plays an important role in dimension reduction techniques, such as reduced basis methods for solving parameter-depende ...
We present and analyze a simple numerical method that diagonalizes a complex normal matrix A by diagonalizing the Hermitian matrix obtained from a random linear combination of the Hermitian and skew-Hermitian parts of A. ...
Various iterative eigenvalue solvers have been developed to compute parts of the spectrum for a large sparse matrix, including the power method, Krylov subspace methods, contour integral methods and preconditioned solvers such as the so-called locally opti ...
In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...
We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different approaches to leve ...
The aim of this work is to develop a fast algorithm for approximating the matrix function f(A) of a square matrix A that is symmetric and has hierarchically semiseparable (HSS) structure. Appearing in a wide variety of applications, often in the context of ...
Interpolation of data on non-Euclidean spaces is an active research area fostered by its numerous applications. This work considers the Hermite interpolation problem: finding a sufficiently smooth manifold curve that interpolates a collection of data point ...
This work considers the low-rank approximation of a matrix (Formula presented.) depending on a parameter (Formula presented.) in a compact set (Formula presented.). Application areas that give rise to such problems include computational statistics and dyna ...
This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...
It is well known that a family of n×n commuting matrices can be simultaneously triangularized by a unitary similarity transformation. The diagonal entries of the triangular matrices define the n joint eigenvalues of the family. In this work, we consider th ...
The numerical solution of the generalized eigenvalue problem for a singular matrix pencil is challenging due to the discontinuity of its eigenvalues. Classically, such problems are addressed by first extracting the regular part through the staircase form a ...
Rational approximation is a powerful tool to obtain accurate surrogates for nonlinear functions that are easy to evaluate and linearize. The interpolatory adaptive Antoulas-Anderson (AAA) method is one approach to construct such approximants numerically. F ...
We examine a method for solving an infinite-dimensional tensor eigenvalue problem (Formula presented.), where the infinite-dimensional symmetric matrix (Formula presented.) exhibits a translational invariant structure. We provide a formulation of this type ...
Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD) for performing t ...
