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.

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 ...

In this paper it is shown that a Lanczos potential for the Weyl curvature tensor does not exist for all spaces of dimension n ≥ 7. Whether there exists a Lanczos potential [1] for Weyl curvature tensors in dimensions n > 4 has still not been determined. Although Lanczos's original proof [1] for existence was flawed [2], there have subsequently been complete proofs for existence in four dimensio...

Given a square matrix and single right and left starting vectors, the classical nonsymmetric Lanczos process generates two sequences of biorthogonal basis vectors for the right and left Krylov subspaces induced by the given matrix and vectors. In this paper, we propose a Lanczos-type algorithm that extends the classical Lanczos process for single starting vectors to multiple starting vectors. G...

Approximations of expressions of the form If := trace(W T f(A)W ), where A ∈ Rm×m is a large symmetric matrix, W ∈ Rm×k with k ≪ m, and f is a function, can be computed without evaluating f(A) by applying a few steps of the global block Lanczos method to A with initial block-vector W . This yields a partial global Lanczos decomposition of A. We show that for suitable functions f upper and lower...

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.

in this work‎, ‎an iterative method based on a matrix form of lsqr algorithm is constructed for solving the linear operator equation $mathcal{a}(x)=b$‎ ‎and the minimum frobenius norm residual problem $||mathcal{a}(x)-b||_f$‎ ‎where $xin mathcal{s}:={xin textsf{r}^{ntimes n}~|~x=mathcal{g}(x)}$‎, ‎$mathcal{f}$ is the linear operator from $textsf{r}^{ntimes n}$ onto $textsf{r}^{rtimes s}$‎, ‎$ma...