Related papers: Rectangular eigenvalue problems
An elimination problem in semidefinite programming is solved by means of tensor algebra. It concerns families of matrix cube problems whose constraints are the minimum and maximum eigenvalue function on an affine space of symmetric…
We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…
In this paper the author introduces a new domain decomposition method for the solution of discretised integral equation eigenvalue problems. The new domain decomposition method is motivated by the so-called automated multi-level…
The problem of iterated partial summations is solved for some discrete distributions defined on discrete supports. The power method, usually used as a computational approach to finding matrix eigenvalues and eigenvectors, is in some cases…
In this paper, we extend the eigenvalue method of the algebraic Riccati equation to the differential Riccati equation (DRE) in contraction analysis. One of the main results is showing that solutions to the DRE can be expressed as functions…
We prove quadratic eigenvalue perturbation bounds for generalized Hermitian eigenvalue problems. The bounds are proportional to the square of the norm of the perturbation matrices divided by the gap between the spectrums. Using the results…
When applying eigenvalue decomposition on the quadratic term matrix in a type of linear equally constrained quadratic programming (EQP), there exists a linear mapping to project optimal solutions between the new EQP formulation where $Q$ is…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian…
Let $\om $ be a bounded domain in an $n$-dimensional Euclidean space $\Bbb R^n$. We study eigenvalues of an eigenvalue problem of a system of elliptic equations: $$ \{\aligned &\Delta {\mathbf u}+ \alpha{\rm grad}(\text{div}{\mathbf…
In this paper we present several additions to the quaternion QR algorithm, including algorithms for eigenvector computation and eigenvalue reordering. A key outcome of the eigenvalue reordering algorithm is that the aggressive early…
The problem of root mean square approximation of a square integrable function by finite linear combinations of exponential functions is considered. It is subdivided into linear and nonlinear parts. The linear approximation problem is…
Often, polynomials or rational functions, orthogonal for a particular inner product are desired. In practical numerical algorithms these polynomials are not constructed, but instead the associated recurrence relations are computed.…
This work introduces a novel algorithm to solve large-scale eigenvalue problems and seek a small set of eigenpairs. The method, called randomized Krylov-Schur (rKS), has a simple implementation and benefits from fast and efficient…
Based on the work of Xu and Zhou [Math.Comput., 69(2000), pp.881-909], we establish new three-level and multilevel finite element discretizations by local defect-correction technique. Theoretical analysis and numerical experiments show that…
This paper studies tensor eigenvalue complementarity problems. Basic properties of standard and complementarity tensor eigenvalues are discussed. We formulate tensor eigenvalue complementarity problems as constrained polynomial…
A new approach to solving eigenvalue optimization problems for large structured matrices is proposed and studied. The class of optimization problems considered is related to computing structured pseudospectra and their extremal points, and…
The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…
The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex,…
A new discretization of the radial equations that appear in the solution of separable second order partial differential equations with some rotational symmetry (as the Schrodinger equation in a central potential) is presented. It cures a…