Block Lanczos algorithm.

Abstract

We use a block Lanczos algorithm for computing a few of the smallest eigenvalues and the corresponding eigenvectors of a large symmetric matrix rather than computing all the eigenvalue-eigenvector pairs. The basic Lanczos algorithm generates a similar matrix which is block tridiagonal from a given large symmetric matrix. The size of the generated tridiagonal matrix depends upon the number of the smallest eigenvalues to be computed. The result is savings in computations and storage. The block Lanczos algorithm is well -suited for problems involving multiple eigenvalues. In this thesis, we develop the block Lanczos algorithm to estimate the direction-of-arrival (DOA) of a point source based on the observations measured at a linear array of sensors and compare the performance with that of a single vector Lanczos algorithm. The results of the computer simulation experiments conducted with this method are presented and discussed.