• ARPACK

  • Referenced in 768 articles [sw04218]
  • package is designed to compute a few eigenvalues and corresponding eigenvectors of a general ... point operations. This software is based upon an algorithmic variant of the Arnoldi process called ... designed to compute a few (k) eigenvalues with user specified features such as those...
  • lobpcg.m

  • Referenced in 115 articles [sw24008]
  • conjugate gradient (LOBPCG) method for symmetric eigenvalue problems, based on a local optimization ... initial guesses. As the “ideal” control algorithm, we advocate the standard preconditioned conjugate gradient method ... linear equations under the assumption that the eigenvalue is known. We recommend that every...
  • Sips

  • Referenced in 9 articles [sw20921]
  • this article, we present a parallel eigenvalue algorithm based on distributed spectrum slicing. We describe...
  • PMIRKDC

  • Referenced in 31 articles [sw06409]
  • Runge-Kutta schemes within a defect control algorithm. The primary computational costs involve the treatment ... software, RSCALE, based on a parallel block eigenvalue rescaling algorithm. Other modifications involve parallelization...
  • FEAST

  • Referenced in 70 articles [sw04025]
  • eigenvalues and eigenvectors within a given search interval. It is based on an innovative fast ... stable numerical algorithm -- named the FEAST algorithm -- which deviates fundamentally from the traditional Krylov subspace ... based techniques (Arnoldi and Lanczos algorithms) or other Davidson-Jacobi techniques. The FEAST algorithm takes ... multiple right-hand sides and one reduced eigenvalue problem orders of magnitude smaller than...
  • QMRPACK

  • Referenced in 77 articles [sw00754]
  • linear systems. QMR is based on the look-ahead Lanczos algorithm that, by itself ... also be used to obtain approximate eigenvalues of large non-Hermitian matrices. QMRPACK...
  • Eigensolve

  • Referenced in 25 articles [sw11986]
  • eigenvalue algorithm for approximating roots of univariate polynomials. The author studies an iterative algorithm that ... iteration is based on floating-point computation of the eigenvalues of a generalized companion matrix ... conditioned polynomials are carefully implemented for the algorithms...
  • Algorithm 854

  • Referenced in 16 articles [sw07345]
  • eigenvalues and invariant subspaces of Hamiltonian and skew-Hamiltonian matrices. The implemented algorithms are based ... symmetry preservation for the computed eigenvalues. These algorithms are supplemented with balancing and block algorithms...
  • MatrixMarket

  • Referenced in 149 articles [sw04020]
  • data for use in comparative studies of algorithms for numerical linear algebra. Matrices as well ... services, from linear systems, least squares, and eigenvalue computations in a wide variety of scientific ... matrices in your Web browser, or form-based requests to generate matrices at the Matrix...
  • SLEIGN2

  • Referenced in 37 articles [sw01230]
  • Algorithm 810: The SLEIGN2 Sturm-Liouville code. The SLEIGN2 code is based on the ideas ... SLEIGN2 code is to compute eigenvalues and eigenfunctions of regular and singular self-adjoint Sturm ... singular case. The code uses some new algorithms, which we describe, and has a driver...
  • ACGSSV

  • Referenced in 6 articles [sw20836]
  • However, the conjugate gradient algorithm ADCG based on clustering the eigenvalues of the iteration matrix ... slightly more robust than our ACGSSV algorithm. By solving five applications from the MINPACK ... that the adaptive Perry conjugate gradient algorithms based on the self-scaling memoryless BFGS update...
  • Algorithm 922

  • Referenced in 29 articles [sw12858]
  • Algorithm 922: A mixed finite element method for Helmholtz transmission eigenvalues. Transmission eigenvalue problem ... adjoint, the computation of transmission eigenvalues needs special treatment. Based on a fourth-order reformulation ... formulation leads to a generalized eigenvalue problem naturally without the need to invert a related ... solve the resulting non-Hermitian eigenvalue problem, an iterative algorithm using restarted Arnoldi method...
  • na25

  • Referenced in 6 articles [sw11492]
  • approximations based on the Newton polygon. The algorithm is implemented as a Fortran 95 module ... Manocha-Demmel approach based on eigenvalue computation. In fact, the algorithm provides better approximations...
  • SERK2

  • Referenced in 8 articles [sw10426]
  • showed that previous codes based on stabilized Runge–Kutta algorithms have some difficulties in solving ... with very large eigenvalues and we derived a new code, SERK2, based on sixth-order ... polynomials. Here, we develop a new method based on second-order polynomials with ... efficiency and accuracy of the new algorithms when compared to other well-known second-order...
  • TenEig

  • Referenced in 17 articles [sw14671]
  • mixed volume. Based on this bound and the structures of tensor eigenvalue problems, we propose ... homotopy continuation type algorithms to solve tensor eigenproblems. With proper implementation, these methods can find...
  • chebop

  • Referenced in 28 articles [sw12693]
  • operator with expm(L) or determine eigenvalues and eigenfunctions with eigs(L). A system ... dimension, based on the previously developed chebfun system in object-oriented Matlab. The algorithms involved...
  • Mixmod

  • Referenced in 35 articles [sw06991]
  • Model-based cluster and discriminant analysis with the MIXMOD software. The Mixture Modeling (MIXMOD) program ... discriminant analysis. A large variety of algorithms to estimate the mixture parameters are proposed ... different assumptions regarding the component variance matrix eigenvalue decomposition. Moreover, different information criteria for choosing...
  • DVDSON

  • Referenced in 16 articles [sw17845]
  • presented for determining a few selected eigenvalues and their eigenvectors on either ... spectrum of a large, real, symmetric matrix. Based on the Davidson method, which is extensively ... implementation improves the power of the original algorithm by adopting several extensions. The matrix-vector...
  • LSTRS

  • Referenced in 26 articles [sw04729]
  • Algorithm 873: LSTRS: MATLAB software for large-scale trust-region subproblems and regularization A MATLAB ... based on a reformulation of the trust-region subproblem as a parameterized eigenvalue problem...
  • Algorithm 800

  • Referenced in 8 articles [sw04405]
  • Algorithm 800. Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices. I: The square ... authors describe a set of LAPACK-based Fortran 77 subroutines for reducing a Hamiltonian matrix ... transformations and for approximating all of its eigenvalues using an implicit version of Van Loan ... needed by the general QR algorithm. Routines are provided for computing the square-reduced form...