On Some Modiications of the Lanczos Algorithm and the Relation with Pad E Approximations

E Approximation of Large - Scaledynamic Systems with Lanczos Methods

The utility of Lanczos methods for the approximation of large-scale dynamical systems is considered. In particular , it is shown that the Lanczos method is a technique for yielding Pad e approximants which has several advantages over more traditional explicit moment matching approaches. An extension of the Lanczos algorithm is developed for computing multi-point Pad e approximations of descript...

The Lanczos Algorithm and Pad E Approximations

An Explicit Formula for Lanczos Polynomials*

The Lanczos algorithm for tridiagonalizing a given matrix A generates a sequence of approximating matrices A, that can naturally be obtained as restrictions to subspaces. The eigenvalues of these approximating matrices are well known to be good approximations to the extreme eigenvalues of A. In this paper we produce explicit formulas for the characteristic polynomials of the A,, in terms of the...

Transpose-free Matrix Pad e Via Lanczos Method

A transpose-free two-sided nonsymmetric Lanczos method is developed for multiple starting vectors on both the left and right. The method is applied to the computation of the matrix Pad e approximation to a linear dynamical system. The result is a method which can be labeled Transpose-Free Matrix Pad e Via Lanczos. The method is mathematically equivalent to the two-sided methods, but avoids the ...

The Unsymmetric Lanczos Algorithms and Their Relations to Pad E Approximation Continued Fractions and the Qd Algorithm

First several algorithms based on the unsymmetric Lanczos process are surveyed the biorthog onalization BO algorithm for constructing a tridiagonal matrix T similar to a given matrix A whose ex treme spectrum is sought typically the BOBC algorithm which generates directly the LU factors of T the Biores Lanczos Orthores Biomin Lanczos Orthomin or biconjugate gradient BCG and the Biodir Lanczos O...