• # LOBPCG

• Referenced in 32 articles [sw09638]
• methods for high-dimensional 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...
• # CIRR

• Referenced in 40 articles [sw12618]
• method with contour integral for generalized eigenvalue problems. We consider a Rayleigh-Ritz type eigensolver ... certain region of generalized eigenvalue problems. When the matrices are very large, iterative methods ... circle that contains relatively small number of eigenvalues is used to construct a subspace. Since...
• # NLEIGS

• Referenced in 30 articles [sw22547]
• fully rational Krylov methods for nonlinear eigenvalue problems. A new rational Krylov method ... efficient solution of nonlinear eigenvalue problems, $A(lambda)x = 0$, is proposed. This iterative method ... fully rational Krylov method for nonlinear eigenvalue problems (abbreviated as NLEIGS), is based on linear ... type linearization for obtaining a generalized eigenvalue problem with special structure. This structure is particularly...
• # PRIMME

• Referenced in 48 articles [sw04023]
• Iterative MultiMethod Eigensolver. Symmetric and Hermitian eigenvalue problems enjoy a remarkable theoretical structure that allows ... engineering, and some QCD applications routinely compute eigenvalues of matrices of dimension more than...
• # ABLE

• Referenced in 33 articles [sw12726]
• Block Lanczos Method for Non-Hermitian Eigenvalue Problems. This work presents an adaptive block Lanczos ... method for large-scale non-Hermitian 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...
• # LSTRS

• Referenced in 30 articles [sw04729]
• LSTRS is designed for large-scale quadratic problems with one norm constraint. The method ... trust-region subproblem as a parameterized eigenvalue problem, and consists of an iterative procedure that ... solution of a large-scale eigenvalue problem at each step. LSTRS relies on matrix-vector...
• # symrcm

• Referenced in 385 articles [sw08566]
• matrices that come from long, skinny problems. The ordering works for both symmetric and nonsymmetric ... real, symmetric sparse matrix, S, the eigenvalues of S(r,r) are the same...
• # EISPACK

• Referenced in 486 articles [sw04208]
• collection of Fortran subroutines that compute the eigenvalues and eigenvectors of nine classes of matrices ... value decomposition to solve certain least-squares problems. EISPACK has been superseded for the most...