The Lanczos algorithm for matrix tridiagonalisation suffers from strong numerical instability in finite precision arithmetic when applied to evaluate matrix eigenvalues. The mechanism by which this instability arises is well documented in the literature. A recent application of the Lanczos algorithm proposed by Bai, Fahey and Golub allows quadrature evaluation of inner products of the form ψ · ...

The Lanczos algorithm is applied to calculate some finite-temperature physical quantities, as well as the ground-state ones. We introduce the finite-temperature Lanczos algorithm and apply it for some current problems in the low-dimensional strongly correlated electron systems; the charge stripe, the pseudogap and phonon-induced anomalous ARPES spectrum in the high-Tc superconducting cuprates.

In theory, the Lanczos algorithm generates an orthogonal basis of corresponding Krylov subspace. However, in finite precision arithmetic orthogonality and linear independence computed vectors is usually lost quickly. this paper we study a class matrices starting having special nonzero structure that guarantees exact computations whenever floating point satisfying IEEE 754 standard used. Analogo...

The symmetric band Lanczos process is an extension of the classical Lanczos algorithm for symmetric matrices and single starting vectors to multiple starting vectors. After n iterations, the symmetric band Lanczos process has generated an n× n projection, Tn, of the given symmetric matrix onto the n-dimensional subspace spanned by the first n Lanczos vectors. This subspace is closely related to...

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.

In this paper we show that the two-sided Lanczos procedure combined with implicit restarts, offers significant advantages over Pad6 approximations used typically for model reduction in circuit simulation. Keywords-Dynamical systems, Model reduction, Numerical methods, Pad6 approximation, Lanczos algorithm.

We present experiments with various solvers for large sparse matrix eigenvalue problems. These problems occur in the computation of a few of the lowest frequencies of standing electromagnetic waves in cavities that have been discretized by the nite element method. The solvers investigated are (1) subspace iteration, (2) block Lanczos algorithm, (3) implicitly restarted Lanczos algorithm and (4)...

The global Lanczos algorithm for solving the RLCG interconnect circuits is presented in this paper. This algorithm is an extension of the standard Lanczos algorithm for multiple-inputs multiple-outputs (MIMO) systems. A new matrix Krylov subspace will be developed first. By employing the congruence transformation with the matrix Krylov subspace, the two-side oblique projection-based method can ...

The nonsymmetric Lanczos algorithm, which belongs to the class of Krylov subspace methods, is increasingly being used for model reduction of large scale systems of the form f(s) = c (sI−A)−1b, to exploit the sparse structure and reduce the computational burden. However, a good approximation is, usually, achieved only with relatively high order reduced models. Moreover, the computational cost of...