LINEAR COMBINATION OF LANCZOS VECTORS - A STORAGE-EFFICIENT ALGORITHMFOR SPARSE-MATRIX EIGENVECTOR COMPUTATIONS

We present a storage-efficient and robust algorithm for the computatio n of eigenvectors of large sparse symmetrical matrices using a Lanczos scheme. The algorithm is based upon a linear combination of Lanczos v ectors (LCLV) with a variable iteration depth. A simple method is give n to determine the iteration depth before the eigenvector computation is performed. Test calculations are reported for tight-binding models of ordered and disordered 2-D systems. The algorithm turns out to be r eliable if an eigenvector residual less than 10(-4) is required. We re port benchmarks for various computers. Possible fields of application are discussed.