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 ...

This paper proposes a harmonic Lanczos bidiagonalization method for computing some interior singular triplets of large matrices. It is shown that the approximate singular triplets are convergent if a certain Rayleigh quotient matrix is uniformly bounded and the approximate singular values are well separated. Combining with the implicit restarting technique, we develop an implicitly restarted ha...

We consider the convergence acceleration of the Krylov-Lanczos interpolation by rational correction functions and investigate convergence of the resultant parametric rational-trigonometric-polynomial interpolation. Exact constants of asymptotic errors are obtained in the regions away from discontinuities, and fast convergence of the rational-trigonometric-polynomial interpolation compared to th...

In part I of this work 10], a rational Lanczos algorithm was developed which led to rational inter-polants of dynamical systems. In this sequel, the important implementational issue of interpolation point selection is analyzed in detail. A residual expression is derived for the rational Lanczos algorithm and is used to govern the placement and type of the interpolation points. Algorithms are de...

We show constructively that, under certain regularity assumptions, any system of coupled linear differential equations with variable coefficients can be tridiagonalized by a time-dependent Lanczos-like method. The proof we present formally establishes the convergence so-called ?-Lanczos algorithm and yields full characterization algorithmic breakdowns. From there, solution original is available...

A general framework for proving error bounds and convergence of a large class of unsymmetric meshless numerical methods for solving well-posed linear operator equations is presented. The results provide optimal convergence rates, if the test and trial spaces satisfy a stability condition. Operators need not be elliptic, and the problems can be posed in weak or strong form without changing the t...

In this paper we present HUND, a hypergraph-based unsymmetric nested dissection ordering algorithm for reducing the fill-in incurred during Gaussian elimination. HUND has several important properties. It takes a global perspective of the entire matrix, as opposed to local heuristics. It takes into account the assymetry of the input matrix by using a hypergraph to represent its structure. It is ...

Motion Estimation (ME) is a critical part of video compression. This paper describes in-depth performance analysis of three most recent motion estimation algorithms based on motion activity in video sequences. Latest H.264/AVC video compression standard has been used for the performance analysis of three types of ME algorithms, which are: Enhances Predictive Zonal Search (EPZS), Unsymmetric-cro...