Fast algorithms, based on the unsymmetric look-ahead Lanczos and the Arnoldi process, are developed for the estimation of the functional (f)= uf(A)v for xed u; v and A, where A∈Rn×n is a large7 scale unsymmetric matrix. Numerical results are presented which validate the comparable accuracy of both approaches. Although the Arnoldi process reaches convergence more quickly in some cases, it 9 has ...

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...

We address the partial realization problem for linear descriptor systems. A general solution to this problem using the Markov parameters of the system defined via its Laurent series is provided. For proper descriptor systems, we also discuss a numerically feasible algorithm for computing a partial minimal realization based on the unsymmetric Lanczos process. Applications to model reduction for ...

In this paper, we investigate a direct and an inverse eigenvalue problem to recover doubly periodic pseudo-Jacobi matrices from three spectra ?, ?1, ?2 two positive numbers ??, ??. Necessary sufficient conditions for the existence of solution are given numerical algorithms, using modified unsymmetric Lanczos scheme, reconstruct matrix prescribed data proposed. Some illustrative examples present...

A Krylov subspace projection method which provides simultaneous solutions of the Helmholtz equation at multiple frequencies in one solution step is presented. The projector is obtained with an unsymmetric block Lanczos algorithm applied to a transfer function derived from a finite element discretization. This approach is equivalent to a matrixvalued Pad e approximation of the transfer function....

Generalized block Lanczos methods for large unsymmetric eigenproblems are presented, which contain the block Arnoldi method, and the block Arnoldi algorithms are developed. The convergence of this class of methods is analyzed when the matrix A is diagonalizable. Upper bounds for the distances between normalized eigenvectors and a block Krylov subspace are derived, and a priori theoretical error...

For the eigenvalues of a large and sparse unsymmetric co-eecient matrix, we have proposed an improved version of the unsymmetric Lanczos process combining elements of numerical stability and parallel algorithm design. The algorithm is derived such that all inner products and matrix-vector multiplications of a single iteration step are independent and communication time required for inner produc...

For the solutions of large and sparse linear systems of equations with unsymmetric coeÆcient matrices, we propose an improved version of the BiConjugate Gradient method (IBiCG) method based on [5, 6] by using the Lanczos process as a major component combining elements of numerical stability and parallel algorithm design. For Lanczos process, stability is obtained by a coupled two-term procedure...

|For the eigenvalues of a large and sparse unsym-metric coeecient matrix, we propose an improved version of the unsymmetric Lanczos process combining elements of numerical stability and parallel algorithm design. Stability is obtained by a coupled two-term recurrences procedure that generates Lanczos vectors scaled to unit length. The algorithm is derived such that all inner products and matrix...