Linear combination of Lanczos vectors: A storage‐efficient algorithm for sparse matrix eigenvector computations
Th. Koslowski, Wolfgang von Niessen · Journal of Computational Chemistry · 1993
Abstract We present a storage‐efficient and robust algorithm for the computation of eigenvectors of large sparse symmetrical matrices using a Lanczos scheme. The algorithm is based upon a linear combination of Lanczos vectors (LCLV) with a variable iteration depth. A simple method is given 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 reliable if an eigenvector residual less than 10−4 is required. We report benchmarks for various computers. Possible fields of application are discussed. © 1993 John Wiley & Sons, Inc.