The Lanczos method and its variants can be used to solve eeciently the rational interpolation problem. In this paper we present a suitable fast modiication of a general look-ahed version of the Lanczos process in order to deal with polynomials expressed in the Chebyshev orthogonal basis. The proposed approach is particularly suited for rational interpolation at Chebyshev points, that is, at the...

Using the work by Bampi and Caviglia, we write the Weyl-Lanczos equations as an exterior differential system. Using Janet-Riquier theory, we compute the Cartan characters for all spacetimes with a diagonal metric and for the plane wave spacetime since all spacetimes have a plane wave limit. We write the Lanczos wave equation as an exterior differential system and, with assistance from Janet-Riq...

We study numerical methods for solving nonlinear elliptic eigenvalue problems which contain folds and bifurcation points. First we present some convergence theory for the MINRES, a variant of the Lanczos method. A multigrid-Lanczos method is then proposed for tracking solution branches of associated discrete problems and detecting singular points along solution branches. The proposed algorithm ...

In this paper, we present new error bounds for the Lanczos method and the shift-andinvert Lanczos method for computing e−τAv for a large sparse symmetric positive semidefinite matrix A. Compared with the existing error analysis for these methods, our bounds relate the convergence to the condition numbers of the matrix that generates the Krylov subspace. In particular, we show that the Lanczos m...

Using the work by Bampi and Caviglia, we write the Weyl-Lanczos equations as an exterior differential system. Using Janet-Riquier theory, we compute the Cartan characters for all spacetimes with a diagonal metric and for the plane wave spacetime since all spacetimes have a plane wave limit. We write the Lanczos wave equation as an exterior differential system and, with assistance from Janet-Riq...

While discussing the convergence of the Lanczos method, Trefethen and Bau observed a relationship with electric charge distributions, and claimed that the Lanczos iteration tends to converge to eigenvalues in regions of \too little charge" for an equilibrium distribution. Recently, Kuijlaars found a theoretical justiication for this phenomenon by considering the Lanczos method applied to a suit...

This paper considers the problem of computing charge densities in a density functional theory (DFT) framework. In contrast to traditional, diagonalization-based, methods, we utilize a technique which exploits a Lanczos basis, without explicit reference to individual eigenvectors. The key ingredient of this new approach is a partial reorthogonalization strategy whose goal is to ensure a good lev...

We study quasistationary physical process for black holes within the context of Lanczos-Lovelock gravity. We show that the Wald entropy of the stationary black holes in Lanczos-Lovelock gravity monotonically increases for quasistationary physical processes in which the horizon is perturbed by the accretion of positive energy matter and the black hole ultimately settles down to a stationary stat...