
LAPACK
 Referenced in 1510 articles
[sw00503]
 solutions of linear systems of equations, eigenvalue problems, and singular value problems. The associated matrix...

ARPACK
 Referenced in 732 articles
[sw04218]
 subroutines designed to solve large scale eigenvalue problems. The package is designed to compute ... eigenvalues and corresponding eigenvectors of a general n by n matrix A. It is most ... technique that is suitable for large scale problems. For many standard problems, a matrix factorization ... designed to compute a few (k) eigenvalues with user specified features such as those...

INTLAB
 Referenced in 356 articles
[sw04004]
 multivariate nonlinear equations (simple and clusters) eigenvalue problems (simple and clusters, also inner inclusions ... structured matrices) generalized eigenvalue problems (simple and clusters) quadrature for univariate functions univariate polynomial zeros...

ScaLAPACK
 Referenced in 380 articles
[sw00830]
 linear equations, least squares problems, and eigenvalue problems. The goals of both projects are efficiency...

HSL
 Referenced in 232 articles
[sw00418]
 linear systems of equations and sparse eigenvalue problems. MATLAB interfaces are offered for selected packages...

SLEPc
 Referenced in 122 articles
[sw00875]
 SLEPc the Scalable Library for Eigenvalue Problem Computations, is a software library for the solution ... singular value decomposition or the quadratic eigenvalue problem...

MatrixMarket
 Referenced in 122 articles
[sw04020]
 SPARSKIT collection, and the Nonsymmetric Eigenvalue Problem (NEP) collection of Bai, Day, Demmel and Dongarra...

CLAPACK
 Referenced in 87 articles
[sw03112]
 linear equations, linear least squares problems, eigenvalue problems, and singular value problems. Designed...

NLEVP
 Referenced in 83 articles
[sw04058]
 NLEVP: A Collection of Nonlinear Eigenvalue Problems. This MATLAB Toolbox provides a collection of nonlinear ... eigenvalue problems. It contains problems from models of reallife applications as well as problems...

libMesh
 Referenced in 106 articles
[sw06657]
 solving both standard and generalized eigenvalue problems...

lobpcg.m
 Referenced in 93 articles
[sw24008]
 conjugate gradient (LOBPCG) method for symmetric eigenvalue problems, based on a local optimization ... linear equations under the assumption that the eigenvalue is known. We recommend that every ... this “ideal” algorithm on our model test problems in terms of the speed of convergence...

RICPAC
 Referenced in 53 articles
[sw15253]
 generalized algebraic Riccati equations. The generalized eigenvalue problem provides a powerful framework for the solution ... form is derived from control and filtering problems for systems in generalized (or implicit ... certain associated Hamiltonian or symplectic generalized eigenvalue problems. Utilizing an embedding technique, the package also ... Ward’s balancing for the generalized eigenvalue problem are available to improve condition and accuracy...

FEAST
 Referenced in 52 articles
[sw04025]
 solving the standard or generalized eigenvalue problem, and obtaining all the eigenvalues and eigenvectors within ... righthand sides and one reduced eigenvalue problem orders of magnitude smaller than the original...

NinfG/MPI
 Referenced in 45 articles
[sw03461]
 hybrid parallel method for large sparse eigenvalue problems on a grid computing environment using Ninf ... hybrid parallel method for large sparse eigenvalue problems in a grid computing environment. A moment...

TRLan
 Referenced in 54 articles
[sw04029]
 situation. For example if the eigenvalue problem may have some symmetry and only a portion...

LOBPCG
 Referenced in 27 articles
[sw09638]
 methods for highdimensional elliptic PDE eigenvalue problems. We consider elliptic PDE eigenvalue problems ... discretized such that the resulting matrix eigenvalue problem Ax=λx exhibits Kronecker product structure ... approaches to the solution of matrix eigenvalue problems fail due to the exponentially growing degrees ... rank variant of LOBPCG, a classical preconditioned eigenvalue solver. We also show...

Algorithm 922
 Referenced in 25 articles
[sw12858]
 method for Helmholtz transmission eigenvalues. Transmission eigenvalue problem has important applications in inverse scattering. Since ... fourthorder reformulation of the transmission eigenvalue problem, a mixed finite element method is applied ... formulation leads to a generalized eigenvalue problem naturally without the need to invert a related ... solve the resulting nonHermitian eigenvalue problem, an iterative algorithm using restarted Arnoldi method...

ABLE
 Referenced in 30 articles
[sw12726]
 Block Lanczos Method for NonHermitian Eigenvalue Problems. This work presents an adaptive block Lanczos ... method for largescale nonHermitian Eigenvalue problems (henceforth the ABLE method). The ABLE method ... order of multiple or clustered eigenvalues. Second, stopping criteria are developed that exploit the semiquadratic ... Each innovation is theoretically justified. Academic model problems and real application problems are solved...