• FEAST

  • Referenced in 78 articles [sw04025]
  • library for solving the standard or generalized eigenvalue problem, and obtaining all the eigenvalues ... multiple right-hand sides and one reduced eigenvalue problem orders of magnitude smaller than...
  • QMRPACK

  • Referenced in 77 articles [sw00754]
  • also be used to obtain approximate eigenvalues of large non-Hermitian matrices. QMRPACK ... other for the computation of eigenvalue approximations. We present some numerical examples from applications where...
  • RICPAC

  • Referenced in 60 articles [sw15253]
  • generalized algebraic Riccati equations. The generalized eigenvalue problem provides a powerful framework for the solution ... 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...
  • CLAPACK

  • Referenced in 89 articles [sw03112]
  • linear equations, linear least squares problems, eigenvalue problems, and singular value problems. Designed...
  • testmatrix

  • Referenced in 79 articles [sw14347]
  • include ones with known inverses or known eigenvalues; ill-conditioned or rank deficient matrices...
  • Gensys

  • Referenced in 77 articles [sw26837]
  • variables. The methods are based on matrix eigenvalue decompositions...
  • Ninf-G/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 ... based method that finds several eigenvalues and their corresponding eigenvectors in a given domain...
  • NAPACK

  • Referenced in 70 articles [sw11666]
  • problems, to perform unconstrained minimization, to compute eigenvalues, eigenvectors, the singular value decomposition...
  • Nek5000

  • Referenced in 64 articles [sw08064]
  • strongest direct and adjoint eigenmodes. The large eigenvalue problems are solved using matrix-free methods...
  • ARMS

  • Referenced in 63 articles [sw00048]
  • given together with the proof that eigenvalues of the preconditioned matrix are close...
  • Algorithm 922

  • Referenced in 31 articles [sw12858]
  • mixed finite element method for Helmholtz transmission eigenvalues. Transmission eigenvalue problem has important applications ... self-adjoint, the computation of transmission eigenvalues needs special treatment. Based on a fourth-order ... reformulation of the transmission eigenvalue problem, a mixed finite element method is applied. The method ... formulation leads to a generalized eigenvalue problem naturally without the need to invert a related...
  • TRLan

  • Referenced in 61 articles [sw04029]
  • type of situation. For example if the eigenvalue problem may have some symmetry and only...
  • PRIMME

  • Referenced in 41 articles [sw04023]
  • PReconditioned Iterative MultiMethod Eigensolver. Symmetric and Hermitian eigenvalue problems enjoy a remarkable theoretical structure that ... engineering, and some QCD applications routinely compute eigenvalues of matrices of dimension more than...
  • NGSolve

  • Referenced in 56 articles [sw13154]
  • value problems, initial-boundary value problems and Eigenvalue problems for the available types of equations...
  • CIRR

  • Referenced in 32 articles [sw12618]
  • Ritz method with contour integral for generalized eigenvalue problems. We consider a Rayleigh-Ritz type ... eigensolver for finding a limited set of eigenvalues and their corresponding eigenvectors in a certain ... region of generalized eigenvalue problems. When the matrices are very large, iterative methods are used ... circle that contains relatively small number of eigenvalues is used to construct a subspace. Since...
  • LOBPCG

  • Referenced in 30 articles [sw09638]
  • rank methods for high-dimensional elliptic PDE eigenvalue problems. We consider elliptic PDE eigenvalue problems ... domain, discretized such that the resulting matrix eigenvalue problem Ax=λx exhibits Kronecker product structure ... standard approaches to the solution of matrix eigenvalue problems fail due to the exponentially growing ... rank variant of LOBPCG, a classical preconditioned eigenvalue solver. We also show...
  • EIGIFP

  • Referenced in 39 articles [sw00235]
  • MATLAB program for computing a few extreme eigenvalues and eigenvectors of the large symmetric generalized ... eigenvalue problem $Ax = \lambda Bx$. It is a black-box implementation of an inverse free...
  • quadeig

  • Referenced in 31 articles [sw11532]
  • algorithm for the complete solution of quadratic eigenvalue problems. We develop a new algorithm ... computation of all the eigenvalues and optionally the right and left eigenvectors of dense quadratic ... problem parameters prior to the computation of eigenvalues, a choice of linearization with favorable conditioning ... reveals and deflates the zero and infinite eigenvalues contributed by singular leading and trailing matrix...
  • COBRA

  • Referenced in 28 articles [sw02211]
  • COBRA) performs this assessment by solving an eigenvalue problem in the form of a linear ... configuration. An initial approximation for the eigenvalue is obtained from a fast second order matrix ... method. In COBRA, this approximate eigenvalue is further refined using a variational principle to obtain ... then applied to a sequence of eigenvalues to estimate the exact eigenvalue using the coarsest...
  • NLEIGS

  • Referenced in 28 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 ... called fully rational Krylov method for nonlinear eigenvalue problems (abbreviated as NLEIGS), is based ... companion-type linearization for obtaining a generalized eigenvalue problem with special structure. This structure...