Related papers: Linearizability of eigenvector nonlinearities
In \emph{Wang et al., A Shifted Laplace Rational Filter for Large-Scale Eigenvalue Problems}, the SLRF method was proposed to compute all eigenvalues of a symmetric definite generalized eigenvalue problem lying in an interval on the real…
In this paper, we discuss approximating the eigenvalue problem of biharmonic equation. We first present an equivalent mixed formulation which admits amiable nested discretization. Then, we construct multi-level finite element schemes by…
The inverse Toeplitz eigenvalue problem (ToIEP) concerns finding a vector that specifies the real-valued symmetric Toeplitz matrix with the prescribed set of eigenvalues. Since phase "calibration" errors in uniform linear antenna arrays…
Let $\left( X,\left\Vert \cdot\right\Vert_{X}\right) $ and $\left( Y,\left\Vert \cdot\right\Vert_{Y}\right) $ be Banach spaces over $\mathbb{R},$ with $X$ uniformly convex and compactly embedded into $Y.$ The inverse iteration method is…
We say that a list of real numbers is "symmetrically realisable" if it is the spectrum of some (entrywise) nonnegative symmetric matrix. The Symmetric Nonnegative Inverse Eigenvalue Problem (SNIEP) is the problem of characterising all…
We propose a numerical method for solving high dimensional fully nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction the solution and its gradient by multi-layer neural…
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…
Despite major advancements in nonlinear programming (NLP) and convex relaxations, most system operators around the world still predominantly use some form of linear programming (LP) approximation of the AC power flow equations. This is…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set…
Multi-objective verification problems of parametric Markov decision processes under optimality criteria can be naturally expressed as nonlinear programs. We observe that many of these computationally demanding problems belong to the…
In this note we consider the continuous Galerkin time stepping method of arbitrary order as a possible discretization scheme of nonlinear initial value problems. In addition, we develop and generalize a well known existing result for the…
We address the problem of computing the eigenvalue backward error of the Rosenbrock system matrix under various types of block perturbations. We establish computable formulas for these backward errors using a class of minimization problems…
In recent years, numerous vision and learning tasks have been (re)formulated as nonconvex and nonsmooth programmings(NNPs). Although some algorithms have been proposed for particular problems, designing fast and flexible optimization…
We distinguish two kinds of piecewise linear functions and provide an interesting representation for a piecewise linear function between two normed spaces. Based on such a representation, we study a fully piecewise linear vector…
Given the $n\times n$ matrix polynomial $P(x)=\sum_{i=0}^kP_i x^i$, we consider the associated polynomial eigenvalue problem. This problem, viewed in terms of computing the roots of the scalar polynomial $\det P(x)$, is treated in…
Nonlinear eigenvalue equations arise naturally in quantum information theory, particularly in the variational quantification of entanglement. In this work, we present a hybrid analytical and numerical framework for evaluating the geometric…
We consider the eigenvalue problem for the case where the input matrix is symmetric and its entries perturb in some given intervals. We present a characterization of some of the exact boundary points, which allows us to introduce an inner…
We consider the uncapacitated three-level lot-sizing and replenishment problem with a distribution structure. In this NP-hard problem, a single production plant sends the produced items to replenish warehouses from where they are dispatched…