In this paper, we consider the sparse eigenvalue problem wherein the goal is to obtain a sparse solution to the generalized eigenvalue problem. We achieve this by constraining the cardinality of the solution to the generalized eigenvalue problem and obtain sparse principal component analysis (PCA

This paper considers the sparse eigenvalue problem, which is to extract dominant (largest) sparse eigenvectors with at most k non-zero components. We propose a simple yet effective solution called truncated power method that can approximately solve the underlying nonconvex optimization problem. A

Abstract — We extend the l0-norm “subspectral ” algorithms developed for sparse-LDA [5] and sparse-PCA [6] to more general quadratic costs such as MSE in linear (or kernel) regression. The resulting ”Sparse Least Squares ” (SLS) problem is also NP-hard, by way of its equivalence to a rank-1 sparse

We describe an efficient implementation and present a performance study of an Algebraic Multi-Level Sub-structuring (AMLS) method for sparse eigenvalue problems. We assess the time and memory requirements associated with the key steps of the algorithm, and compare it with the shift

We investigate the sparse eigenvalue problem which arises in various fields such as machine learning and statistics. Unlike standard approaches relying on approximation of the l0norm, we work with an equivalent reformulation of the problem at hand as a DC program. Our starting point

Abstract. This paper surveys numerical methods for general sparse nonlinear eigenvalue problems with special emphasis on iterative projection methods like Jacobi–Davidson, Arnoldi or rational Krylov methods and the automated multi–level substructuring. We do not review the rich literature

An important problem in scientific computing consists in finding a few eigenvalues and corresponding eigenvectors of a very large and sparse matrix. The most popular methods to solve these problems are based on projection techniques on appropriate subspaces. The main attraction of these methods

The Davidson method is extensively used in quantum chemistry and atomic physics for finding a few extreme eigenpairs of a large, sparse, symmetric matrix. It can be viewed as a preconditioned version of the Lanczos method which reduces the number of iterations at the expense of a more complicated

: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 2.2 The equations : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 2.3 Reformulation as a fixed point problem : : : : : : : : : : : : : : : : : : : 13 2.4 The Eigenvalue Problem for Schrodinger's Equation : : : : : : : : : : : : 16 2.5 The Solution of the Nonlinear Poisson

We discuss several techniques for finding leading eigenvalues and eigenvectors for large sparse matrices. The techniques are demonstrated on a scalar Helmholtz equation derived from a model semiconductor rib waveguide problem. We compare the simple inverse iteration approach with more sophisticated