Related papers: Generalized Eigenvalue Problems with Specified Eig…
The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
Pole-swapping algorithms, generalizations of bulge-chasing algorithms, have been shown to be a viable alternative to the bulge-chasing QZ algorithm for solving the generalized eigenvalue problem for a matrix pencil A - {\lambda}B. It is…
We study the existence and localization of eigenvalue-eigenfunction pairs for parameter-dependent Neumann BVPs with a functional term. By reformulating the problems as a Hammerstein integral equation, we apply an existence and localization…
In the Escherization problem, given a closed figure in a plane, the objective is to find a closed figure that is as close as possible to the input figure and tiles the plane. Koizumi and Sugihara's formulation reduces this problem to an…
The rectangular multiparameter eigenvalue problem (RMEP) involves rectangular coefficient matrices (usually with more rows than columns) and may potentially have no solution in its original form. A minimal perturbation framework is proposed…
A shape optimization problem arising from the optimal reinforcement of a membrane by means of one-dimensional stiffeners or from the fastest cooling of a two-dimensional object by means of ``conducting wires'' is considered. The criterion…
Assume that the eigenvalues of a finite hermitian linear operator have been deduced accurately but the linear operator itself could not be determined with precision. Given a set of eigenvalues $\lambda$ and a hermitian matrix $M$, this…
Automated per-instance algorithm selection and configuration have shown promising performances for a number of classic optimization problems, including satisfiability, AI planning, and TSP. The techniques often rely on a set of features…
We derive exact analytic expressions for the distributions of eigenvalues and singular values for the product of an arbitrary number of independent rectangular Gaussian random matrices in the limit of large matrix dimensions. We show that…
We give formulae for first and second derivatives of generalized eigenvalues/eigenvectors of symmetric matrices and generalized singular values/singular vectors of rectangular matrices when the matrices are linear or nonlinear functions of…
We consider the problem of minimising the $L^\infty$ norm of a function of the hessian over a class of maps, subject to a mass constraint involving the $L^\infty$ norm of a function of the gradient and the map itself. We assume zeroth and…
This note introduces a new analytic approach to the solution of a very general class of finite-horizon optimal control problems formulated for discrete-time systems. This approach provides a parametric expression for the optimal control…
In this article we generalize the classic "farm pen" optimization problem from a first course in calculus in a handful of different ways. We describe the solution to an $n$-dimensional rectangular variant, and then study the situation when…
This paper presents an efficient parallel direct algorithm with near-optimal complexity for the compact fourth and sixth-order approximation of the three-dimensional Helmholtz equations [1] with the problem coefficient depending on only one…
Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several…
We address an optimal reachability problem for a planar manipulator in a constrained environment. After introducing the optmization problem in full generality, we practically embed the geometry of the workspace in the problem, by…
In this paper, we discuss numerical approximation of the eigenvalues of the one-dimensional radial Schr\"{o}dinger equation posed on a semi-infinite interval. The original problem is first transformed to one defined on a finite domain by…
The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions.…
Reliable and efficient computation of the pseudospectral abscissa in the large-scale setting is still not settled. Unlike the small-scale setting where there are globally convergent criss-cross algorithms, all algorithms in the large-scale…