In this paper, we propose an implicitly restarted block Lanczos bidiagonalization (IRBLB) method for computing a few extreme or interior singular values and associated right and left singular vectors of a large matrix A. Our method combines the advantages of a block routine, implicit shifting, and the application of Leja points as shifts in the accelerating polynomial. The method neither requir...

Though the implicitly restarted Arnoldi/Lanczos method in ARPACK is a reliable method for computing a few eigenvalues of large-scale matrices, it can be inefficient because it only checks for convergence at restarts. Significant savings in runtime can be obtained by checking convergence at each Lanczos iteration. We describe a new convergence test for the maximum eigenvalue that is numerically ...

The generalized eigenvalue problem for a symmetric definite matrix pencil obtained from finite-element modeling of electroelastic materials is solved numerically by the Lanczos algorithm. mass singular in considered problem, and therefore process proceeds with semi-inner product defined this matrix. shift-and-invert algorithm used to find multiple eigenvalues closest some shift corresponding ei...

We present a new approach for the direct ~and correct! calculation of thermal rate constants k(T) ~‘‘direct’’ meaning that one avoids having to solve the state-to-state reactive scattering problem, and ‘‘correct’’ meaning that the method contains no inherent approximations!. The rate constant is obtained from the long time limit of the flux-position correlation function, Cf ,s(t), whose calcula...

When discussing the convergence properties of the Lanczos iteration method for the real symmetric eigenvalue problem, Trefethen and Bau noted that the Lanczos method tends to find eigenvalues in regions that have too little charge when compared to an equilibrium distribution. In this paper a quantitative version of this rule of thumb is presented. We describe, in an asymptotic sense, the region...

When discussing the convergence properties of the Lanczos iteration method for the real symmetric eigenvalue problem, Trefethen and Bau noted that the Lanczos method tends to find eigenvalues in regions that have too little charge when compared to an equilibrium distribution. In this paper a quantitative version of this rule of thumb is presented. We describe, in an asymptotic sense, the region...

In this paper the new theoretical error bounds on the convergence of the Lanczos and the block-Lanczos methods are established based on results given by Saad. Similar further inequalities are found for the eigenele-ments by using bounds on the acute angle between the exact eigenvectors and the Krylov subspace spanned by x0; Ax0; ; A n?1 x0, where x0 is the initial starting vector of the process...

Abstract We perform time-dependent calculations of single-photon two-electron ionization of the aligned H2 molecule by an XUV pulse. Solution of the time-dependent Schröding equation is sought in spherical coordinates on a radial grid by time propagation using the Arnoldi-Lanczos method. From these calculations, we derive the total integrated as well as fully differential ionization crosssectio...

For most unsymmetric matrices it is difficult to compute many accurate eigenvalues using the primitive form of the unsymmetric Lanczos algorithm (ULA). In this paper we propose a modification of the ULA. It is related to ideas used in [J. Chem. Phys. 122 (2005), 244107 (11 pages)] to compute resonance lifetimes. Using the refined ULA we suggest, the calculation of accurate extremal and interior...