The Lanczos algorithm is evaluated for solving the time-independent as well as the time-dependent Dirac equation with arbitrary electromagnetic fields. We demonstrate that the Lanczos algorithm can yield very precise eigenenergies and allows very precise time propagation of relativistic wave packets. The unboundedness of the Dirac Hamiltonian does not hinder the applicability of the Lanczos alg...

This paper presents an error analysis of the Lanczos algorithm in finite-precision arithmetic for solving the standard nonsymmetric eigenvalue problem, if no breakdown occurs. An analog of Paige's theory on the relationship between the loss of orthogonality among the Lanczos vectors and the convergence of Ritz values in the symmetric Lanczos algorithm is discussed. The theory developed illustra...

An advanced non-linear cascading filter algorithm for the removal of high density salt and pepper noise from the digital images is proposed. The proposed method consists of two stages. The first stage Decision base Median Filter (DMF) acts as the preliminary noise removal algorithm. The second stage is either Modified Decision Base Partial Trimmed Global Mean Filter (MDBPTGMF) or Modified Decis...

This report presents an experimental comparison of NAG Fortran Library software for the solution of large sparse unsymmetric linear systems of algebraic equations Preconditioned RGMRES CGS and Bi CGSTAB methods to be introduced at Mark are compared against one another and against direct methods Test problems include discrete approximations to D elliptic partial di erential equations random valu...

Sparse matrix factorization algorithms are typically characterized by irregular memory access patterns that limit their performance on parallel-vector supercomputers. For symmetric problems, methods such as the multifrontal method replace irregular operations with dense matrix kernels. However, no e cient method based primarily on dense matrix kernels exists for matrices whose pattern is very u...

The Lanczos process constructs a sequence of orthonormal vectors vm spanning a nested sequence of Krylov subspaces generated by a hermitian matrix A and some starting vector b. In this paper we show how to cheaply recover a secondary Lanczos process, starting at an arbitrary Lanczos vector vm and how to use this secondary process to efficiently obtain computable error estimates and error bounds...

The utility of Lanczos methods for the approximation of large-scale dynamical systems is considered. In particular , it is shown that the Lanczos method is a technique for yielding Pad e approximants which has several advantages over more traditional explicit moment matching approaches. An extension of the Lanczos algorithm is developed for computing multi-point Pad e approximations of descript...

The eeciency of solving sparse linear systems on parallel processors and more complex multicluster architectures such as Cedar is greatly enhanced if relatively large grain computational tasks can be assigned to each cluster or processor. The ordering of a system into a bordered block upper triangular form facilitates a reasonable large-grain partitioning. A new algorithm which produces this fo...

In this paper, a combined fuzzy logic and unsymmetric trimmed median filter approach is proposed to remove the high density salt and pepper noise in gray scale and colour images. This algorithm is a combination of decision based unsymmetrical trimmed median filter and fuzzy thresholding technique to preserve edges and fine details in an image. The decision based unsymmetric trimmed median filte...

A dinuclear Rh(− i )/Rh( ) complex bridged by tridentate phosphinine ligands was prepared reduction of the corresponding Rh( complex. An unsymmetric bridging mode differentiated electronic environments Rh centres.