The Lanczos method is often used to solve a large scale symmetric matrix eigen-value problem. It is well-known that the single-vector Lanczos method can only find one copy of any multiple eigenvalue and encounters slow convergence towards clustered eigenvalues. On the other hand, the block Lanczos method can compute all or some of the copies of a multiple eigenvalue and, with a suitable block s...

This work presents a parallel implementation of Lanczos algorithm for SVD Computation using MPI. We investigate execution time as a function of matrix sparsity, matrix size, and the number of processes. We observe speedup and slowdown for parallelized Lanczos algorithm. Reasons for the speedups and the slowdowns are discussed in the report.

The Lanczos algorithm (LA) is a useful iterative method for the reduction of a large matrix to tridiagonal form. It is a storage efficient procedure requiring only the preceding two Lanczos vectors to compute the next. The quasi-minimal residual (QMR) method is a powerful method for the solution of linear equation systems, Ax = b. In this report we provide another application of the QMR method:...

A convergence analysis for the nonsymmetric Lanczos algorithm is presented. By using a tridiagonal structure of the algorithm, some identities concerning Ritz values and Ritz vectors are established and used to derive approximation bounds. In particular, the analysis implies the classical results for the symmetric Lanczos algorithm.

The Biorthogonal Lanczos and the Biconjugate Gradients methods have been proposed as iterative methods to approximate the solution of nonsymmetric and indefinite linear systems. Sonneveld [19] obtained the Conjugate Gradient Squared by squaring the matrix polynomials of the Biconjugate Gra­ dients method. Here we square the Biorthogonal Lanczos, the Biconjugate Residual and the Biconjugate Orth...

An unsymmetric tetracarboxylic ligand collaborates with 4,4'-bipyridine to induce spontaneous resolution to form homochiral 3D coordination frameworks, while the use of longer dipyridyl ligands instead of 4,4'-bipyridine leads to isoreticular but heterochiral frameworks.

This article describes one-pot synthesis of new fluorinated hexahydroquinoline derivatives via unsymmetric Hantzsch reaction involving 5-trifluoromethyl-1,3cyclohexanedione, aldehydes, acetoacetate ester, and ammonium acetate in trifluoroethanol (TFE). The reaction is simple and rapid with high yield.