
UTV
 Referenced in 225 articles
[sw05213]
 rankrevealing 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 125 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 quasiminimal residual (QMR) algorithm is a Krylovsubspace method for the iterative ... based on the lookahead 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 twoterm lookahead 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 75 articles
[sw04025]
 subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other DavidsonJacobi techniques. The FEAST...

SDPT3
 Referenced in 597 articles
[sw04009]
 improve the efficiency and stability of the algorithm are incorporated. For example, steplengths 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 nearbreakdown 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 774 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 nonHermitian Lanczos algorithm. There are three innovations. First, an adaptive ... wellknown 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 298 articles
[sw08225]
 fast Lanczostype 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 27 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]
 nearbreakdown in the CGS algorithm. Lanczos’ method for solving the system of linear equationsAx ... computed recursively. The conjugate gradient squared algorithm (CGS) consists in takingr...

aTRLan
 Referenced in 11 articles
[sw20135]
 TRLan. ThickRestart 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 timeindependent ... 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 matrixvector ... 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 43 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...