• UTV

  • Referenced in 219 articles [sw05213]
  • rank-revealing VSV decompositions, we expand the algorithms for the ULLV decomposition of a matrix ... provide a robust and reliable Lanczos algorithm which -- despite its simplicity is -- able to capture...
  • tn

  • Referenced in 123 articles [sw05140]
  • stationary point. The above mentioned modified Lanczos algorithm requires up to n iterations to compute...
  • QMRPACK

  • Referenced in 77 articles [sw00754]
  • algorithms. The quasi-minimal residual (QMR) algorithm is a Krylov-subspace method for the iterative ... based on the look-ahead Lanczos algorithm that, by itself, can also be used ... with Fortran 77 implementations of the QMR algorithm and variants thereof, and of the three ... coupled two-term look-ahead Lanczos algorithms. In this article, we discuss some...
  • PROPACK

  • Referenced in 96 articles [sw04019]
  • routines are based on the Lanczos bidiagonalization algorithm with partial reorthogonalization (BPRO). The Lanczos routines...
  • FEAST

  • Referenced in 74 articles [sw04025]
  • subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other Davidson-Jacobi techniques. The FEAST...
  • SDPT3

  • Referenced in 592 articles [sw04009]
  • improve the efficiency and stability of the algorithm are incorporated. For example, step-lengths associated ... with semidefinite cones are calculated via the Lanczos method. Numerical experiments show that this general...
  • na1

  • Referenced in 51 articles [sw11516]
  • Avoiding breakdown and near-breakdown in Lanczos type algorithms. The paper deals with methods which ... different from zero but small in Lanczos type algorithms for solving linear systems.par In particular ... existing orthogonal polynomials in the Lanczos type algorithms. The methods described in the paper...
  • ARPACK

  • Referenced in 770 articles [sw04218]
  • operations. This software is based upon an algorithmic variant of the Arnoldi process called ... reduces to a variant of the Lanczos process called the Implicitly Restarted Lanczos Method (IRLM...
  • ABLE

  • Referenced in 31 articles [sw12726]
  • block version of the non-Hermitian Lanczos algorithm. There are three innovations. First, an adaptive ... well-known technique from the Hermitian Lanczos algorithm is generalized to monitor the loss ... biorthogonality and maintain semibiorthogonality among the computed Lanczos vectors. Each innovation is theoretically justified. Academic...
  • CGS

  • Referenced in 297 articles [sw08225]
  • fast Lanczos-type solver for nonsymmetric linear systems The presented method is a combination ... algorithm (a “squared” conjugate gradient method) with a preconditioning called ILLU (an incomplete line...
  • CMRH

  • Referenced in 26 articles [sw02194]
  • linear systems based on the Hessenberg reduction algorithm. The generalized minimal residual (GMRES) methods ... Arnoldi process while QMR uses the Lanczos algorithm for constructing a basis of the Krylov ... Hessenberg process instead of the Lanczos process. We call the new method the CMRH method...
  • na5

  • Referenced in 24 articles [sw11489]
  • near-breakdown in the CGS algorithm. Lanczos’ method for solving the system of linear equationsAx ... computed recursively. The conjugate gradient squared algorithm (CGS) consists in takingr...
  • a-TRLan

  • Referenced in 11 articles [sw20135]
  • TRLan. Thick-Restart Lanczos algorithm is an explicitly restarted Lanczos algorithm for eigenvalue problems...
  • BLZPACK

  • Referenced in 14 articles [sw13005]
  • Fortran 77 implementation of the block Lanczos algorithm intended for the solution of the standard...
  • Dirac_Laczos

  • Referenced in 2 articles [sw16747]
  • methods for the Dirac equation. The Lanczos algorithm is evaluated for solving the time-independent ... electromagnetic fields. We demonstrate that the Lanczos algorithm can yield very precise eigenenergies and allows ... hinder the applicability of the Lanczos algorithm. As the Lanczos algorithm requires only matrix-vector ... parallel implementation of the Dirac Lanczos propagator utilizing the Message Passing Interface standard...
  • LASO2

  • Referenced in 3 articles [sw28488]
  • band matrix generated by the Lanczos algorithm. It also monitors all the eigenvalues of interest...
  • Algorithm 919

  • Referenced in 42 articles [sw07350]
  • Appearing in Exponential Integrators. We develop an algorithm for computing the solution of a large ... constructing a Krylov subspace using Arnoldi or Lanczos iteration and projecting the function on this ... Krylov subspace from growing too large. The algorithm is fully adaptive: it varies both...
  • BiCOR

  • Referenced in 11 articles [sw06491]
  • linear systems. These algorithms are developed from variants of the nonsymmetric Lanczos method. The convergence ... methods under examination with other common iterative algorithms for solving nonsymmetic linear systems...
  • CORS

  • Referenced in 11 articles [sw06493]
  • linear systems. These algorithms are developed from variants of the nonsymmetric Lanczos method. The convergence ... methods under examination with other common iterative algorithms for solving nonsymmetic linear systems...
  • HPEC

  • Referenced in 1 article [sw03700]
  • parallel block Lanczos algorithm and its implementation for the evaluation of some eigenvalues of large ... implements an efficient and portable block Lanczos algorithm for distributed memory multicomputers. HPEC is based...