na18

Implementation of a variable block Davidson method with deflation for solving large sparse eigenproblems. E. R. Davidson’s method [J. Comput Phys. 17, 87-94 (1975; Zbl 0293.65022)] is a preconditioned eigenvalue technique aimed at computing a few of the extreme leftmost or rightmost eigenpairs of a large symmetric matrix. This paper contains a description of a software package that implements a deflated and variable-block version of the Davidson method. The authors do not address performance using parallel computers. The package description is extensive, containing pseudo-code summaries of the primary algorithms, summaries of the input parameters, an architectural description of the software package. It also contains summaries of numerical tests with results comparisons to a dense matrix algorithm in the commercial MATLAB program and to the ARPACK sparse eigenvalue package. The software package contains both the computational routines that carry out the Davidson method and also the support routines that make the software useful as a self-contained package accessible to the end user. Its calculational strategy is controlled through an input file identifying the matrix file name and format, block size, number of desired extreme eigenpairs, and choice of corrector. It is designed to handle three of the most popular sparse matrix storage formats: Harwell-Boeing, compressed column storage, and coordinates. Input and output consists of simple files. The paper includes results of application of the package to twenty-four matrices from the Harwell-Boeing collection. The results were generated on a single-processor SGI Power Challenge computer and speed and accuracy comparisons are presented with MATLAB and ARPACK results (netlib numeralgo na18)