Analysis and development of restarted Krylov subspace methods for computing f(A)b have proliferated in recent years. We present an acceleration technique for such methods when applied to Stieltjes functions f and Hermitian positive definite matrices A. This technique is based on a rank-one modification of the Lanczos matrix derived from a connection between the Lanczos process and Gauss–Radau q...

We use a recently developed technique, which allows to perform few Lanczos steps on a given wavefunction even for large system sizes, to investigate the t−J model in the physical parameter region and to check the stability of the BCS d-wave variational wavefunction [1]. Our statistical Lanczos algorithm, which extends and improves the one Lanczos step proposed in Ref. [2], has been extensively ...

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...

We give a systolic algorithm and array for bidiagonalization of an n x n matrix in O(nlog, n) time, using O(n2) cells. Bandedness of the input matrix may be effectively exploited. If the matrix is banded, with p nonzero subdiagonals and q nonzero superdiagonais, then 4n In(p + q) + O(n) clocks and 2n(p + q ) + O((p + q)’ + n) cells are needed. This is faster than the best previously reported re...

With the increasing use of high-resolution multimedia streams and large image and video archives in many of today’s research and application areas, there is a growing need for multimedia-oriented highperformance computing. As a consequence, a need for algorithms, methodologies, and tools that can serve as support in the (automatic) parallelization of multimedia applications is rapidly emerging....

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...