Related papers: Solving singular generalized eigenvalue problems. …
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
This paper has proposed the GMRES that augments Krylov subspaces with a set of approximate right singular vectors. The proposed method suppresses the error norms of a linear system of equations. Numerical experiments comparing the proposed…
The eigenvalue problem plays a central role in linear algebra and its applications in control and optimization methods. In particular, many matrix decompositions rely upon computation of eigenvalue-eigenvector pairs, such as diagonal or…
We propose new iterative methods for computing nontrivial extremal generalized singular values and vectors. The first method is a generalized Davidson-type algorithm and the second method employs a multidirectional subspace expansion…
Irregular features disrupt the desired classification. In this paper, we consider aggressively modifying scales of features in the original space according to the label information to form well-separated clusters in low-dimensional space.…
Many real-world problems rely on finding eigenvalues and eigenvectors of a matrix. The power iteration algorithm is a simple method for determining the largest eigenvalue and associated eigenvector of a general matrix. This algorithm relies…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
Equations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses…
We propose a new method to solve the eigen-value problem with a two-center single-particle potential. This method combines the usual matrix diagonalization with the method of separable representation of a two-center potential, that is, an…
We introduce a definition of strong hyperbolicity for second order partial differential equations using second order pencils. We show that this definition is equivalent to the standard one, derived by reducing the equations to first order…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…
One-class recognition is traditionally approached either as a representation learning problem or a feature modeling problem. In this work, we argue that both of these approaches have their own limitations; and a more effective solution can…
Pencils of Hankel matrices whose elements have a joint Gaussian distribution with nonzero mean and not identical covariance are considered. An approximation to the distribution of the squared modulus of their determinant is computed which…
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…
The stated paper is dedicated to one of the inverse problems of spectral theory. It is necessary to define matrix (constant) coefficients of some quadratic pencil, if the eigenvalues of this pencil are known. Furthermore, it is known that…
In this paper a robust second-order method is developed for the solution of strongly convex l1-regularized problems. The main aim is to make the proposed method as inexpensive as possible, while even difficult problems can be efficiently…
In this manuscript, a generalized inverse eigenvalue problem is considered that involves a linear pencil $(z\mathcal{J}_{[0,n]}-\mathcal{H}_{[0,n]})$ of matrices arising in the theory of rational interpolation and biorthogonal rational…
Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…
Eigenvalue and eigenpair backward errors are computed for matrix pencils arising in optimal control. In particular, formulas for backward errors are developed that are obtained under block-structure-preserving and…
Recently, a kind of eigensolvers based on contour integral were developed for computing the eigenvalues inside a given region in the complex plane. The CIRR method is a classic example among this kind of methods. In this paper, we propose a…