Related papers: New Power Method for Solving Eigenvalue Problems

The study of solving the inverse eigenvalue problem for nonnegative matrices has been around for decades. It is clear that an inverse eigenvalue problem is trivial if the desirable matrix is not restricted to a certain structure. Provided…

We study the eigenvalue problem for some special class of anti-triangular matrices. Though the eigenvalue problem is quite classical, as far as we know, almost nothing is known about properties of eigenvalues for anti-triangular matrices.…

The sparse generalized eigenvalue problem arises in a number of standard and modern statistical learning models, including sparse principal component analysis, sparse Fisher discriminant analysis, and sparse canonical correlation analysis.…

We present a new algorithm for solving an eigenvalue problem for a real symmetric arrowhead matrix. The algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in $O(n^{2})$…

We present a dynamic algorithm for maintaining $(1+\epsilon)$-approximate maximum eigenvector and eigenvalue of a positive semi-definite matrix $A$ undergoing \emph{decreasing} updates, i.e., updates which may only decrease eigenvalues.…

Rational filter functions can be used to improve convergence of contour-based eigensolvers, a popular family of algorithms for the solution of the interior eigenvalue problem. We present a framework for the optimization of rational filters…

We present a finite difference method to compute the principal eigenvalue and the corresponding eigenfunction for a large class of second order elliptic operators including notably linear operators in nondivergence form and fully nonlinear…

In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image-processing, graph partition and classification, nonlinear physics and more. The canonical eigenproblem we…

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.…

The singular value decomposition (SVD) allows to write a matrix as a product of a left singular vectors matrix, a nonnegative singular values diagonal matrix and a right singular vectors matrix. Among the applications of the SVD are the…

The eigenvalue problem is a fundamental problem in scientific computing. In this paper, we first give the error analysis for a single step or sweep of Jacobi's method in floating point arithmetic. Then we propose a mixed precision…

We propose a numerical method for evaluating eigenvalues and eigenfunctions of Schr\"odinger operators with general confining potentials. The method is selective in the sense that only the eigenvalue closest to a chosen input energy is…

Variational inequalities can in general support distinct solutions. In this paper we study an algorithm for computing distinct solutions of a variational inequality, without varying the initial guess supplied to the solver. The central idea…

The main of this work is to use the unit lower triangular matrices for solving inverse eigenvalue problem of nonnegative matrices and present the easier method to solve this problem.

We present SPEC-RE, a new algorithm to sort complex eigenvalues, generated as the solutions to algebraic equations, whose coefficients are analytic functions of one or many, possibly complex parameters. The fact that the eigenvalues are…

We present a new algorithm for solving an eigenvalue problem for a real symmetric matrix which is a rank-one modification of a diagonal matrix. The algorithm computes each eigenvalue and all components of the corresponding eigenvector with…

We present a novel method to estimate the dominant eigenvalue and eigenvector pair of any non-negative real matrix via graph infection. The key idea in our technique lies in approximating the solution to the first-order matrix ordinary…

It is shown that the problem of balancing a nonnegative matrix by positive diagonal matrices can be recast as a constrained nonlinear multiparameter eigenvalue problem. Based on this equivalent formulation some adaptations of the power…

Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…

Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive for high-dimensional problems. Iterative random sparsification methods allow for the estimation of a single dominant eigenvalue at reduced cost by…