The Lanczos eigensolution takes the dominant amount of time in most normal modes and modal frequency response analyses. This paper introduces a way to reduce the elapsed time of large eigenvalue jobs by using a newly developed parallel option within the Lanczos algorithm. We will compare the performance of the frequency domain decomposition based distributed memory parallel method introduced in...

A new iterative time-reversal algorithm capable of identifying and focusing on multiple scatterers in a relatively small number of iterations is developed. It is recognized that the traditional iterated time-reversal method is based on utilizing power iterations to determine the dominant eigenpairs of the time-reversal operator. The convergence properties of these iterations are known to be sub...

This note explores sparse matrix dense matrix (SMDM) multiplications, useful in block Krylov or block Lanczos methods. SMDM computations are AU , and V A, multiplication of a large sparse matrix m × n matrix A by a matrix V of k rows of length m or a matrix U of k columns of length k, k << m, k << n . In a block Lanczos or Krylov algorithm, matrix matrix multiplications with the ”tall” U and ”w...

Block algorithms have better performance than scalar and single vector algorithms due to their exploitation of memory hierarchy. This paper presents a high performance C implementation of a block Lanczos tridiagonalization algorithm for complex symmetric matrices. The design principles of the implementation and techniques used in the implementation are described. Our experiments show that this ...

This paper describes a highly e cient algorithm for the iterative computation of dominant poles and zeros of large linear networks. The algorithm is based on a new implementation of the Pad e approximation via the Lanczos process. This implementation has superior numerical properties, maintains the same computational e ciency as its predecessors, and provides a bound on the approximation error.

The Lanczos algorithm (LA) is a useful iterative method for the reduction of a large matrix to tridiagonal form. It is a storage efficient procedure requiring only the preceding two Lanczos vectors to compute the next. The quasi-minimal residual (QMR) method is a powerful method for the solution of linear equation systems, Ax = b. In this report we provide another application of the QMR method:...

In this paper we propose a new quadrature scheme for computing vibrational spectra and apply it, using a Lanczos algorithm, to CH(3)CN. All 12 coordinates are treated explicitly. We need only 157'419'523 quadrature points. It would not be possible to use a product Gauss grid because 33 853 318 889 472 product Gauss points would be required. The nonproduct quadrature we use is based on ideas of ...