Related papers: Efficient solution of symmetric eigenvalue problem…
Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…
In energy management, it is common that strategic investment decisions (storage capacity, production units) are made at a slow time scale, whereas operational decisions (storage, production) are made at a fast time scale: for such problems,…
A multilevel correction scheme is proposed to solve defective and nodefective of nonsymmetric partial differential operators by the finite element method. The method includes multi correction steps in a sequence of finite element spaces. In…
The analysis of diagonalizable matrices in terms of their so-called isospectral reduction represents a versatile approach to the underlying eigenvalue problem. Starting from a symmetry of the isospectral reduction, we show in the present…
This paper introduces a simple variant of the power method. It is shown analytically and numerically to accelerate convergence to the dominant eigenvalue/eigenvector pair; and, it is particularly effective for problems featuring a small…
The term interlacing refers to systematic inequalities between the sequences of eigenvalues of two operators defined on objects related by a specific oper- ation. In particular, knowledge of the spectrum of one of the objects then implies…
In this article, we study eigenvalue problems associated to self-adjoint operators and their approximation obtained by subspace projection, as used in the reduced basis method for instance. We provide error bounds between the exact…
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Integral equations are commonly encountered when solving complex physical problems. Their discretization leads to a dense kernel matrix that is block or hierarchically low-rank. This paper proposes a new way to build a low-rank…
The efficient inversion of matrix polynomials is a critical challenge in computational mathematics. We design a procedure to determine the inverse of matrices polynomial of multidimensional Laplace matrices. The method is based on…
In this paper we discuss reduced order models for the approximation of parametric eigenvalue problems. In particular, we are interested in the presence of intersections or clusters of eigenvalues. The singularities originating by these…
Solving eigenproblem of the Laplacian matrix of a fully connected weighted graph has wide applications in data science, machine learning, and image processing, etc. However, this is very challenging because it involves expensive matrix…
Finding sparse solutions of underdetermined systems of linear equations is a fundamental problem in signal processing and statistics which has become a subject of interest in recent years. In general, these systems have infinitely many…
We consider the minimization or maximization of the $J$th largest eigenvalue of an analytic and Hermitian matrix-valued function, and build on Mengi et al. (2014, SIAM J. Matrix Anal. Appl., 35, 699-724). This work addresses the setting…
We present a perturbed subspace iteration algorithm to approximate the lowermost eigenvalue cluster of an elliptic eigenvalue problem. As a prototype, we consider the Laplace eigenvalue problem posed in a polygonal domain. The algorithm is…
In this paper, we propose two iterative methods for finding a common solution of a finite family of equilibrium problems for pseudomonotone bifunctions. The first is a parallel hybrid extragradient-cutting algorithm which is extended from…
Block tridiagonal matrices arise in applied mathematics, physics, and signal processing. Many applications require knowledge of eigenvalues and eigenvectors of block tridiagonal matrices, which can be prohibitively expensive for large…
We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract…
The data input model is a fundamental component of every quantum algorithm, as its efficiency is crucial for achieving potential speed-ups over classical methods. For quantum linear algebra tasks that utilize quantum eigenvalue or singular…
We study two fundamental optimization problems: (1) scaling a symmetric positive definite matrix by a positive diagonal matrix so that the resulting matrix has row and column sums equal to 1; and (2) minimizing a quadratic function subject…