Extracting more than a few eigenvectors from a dense real symmetric matrix: Optimal algorithms versus the architectural constraints of the FPS-X64

Abstract

Ten widely available sets of routines, including HQRII, QCPE GIVENS and EISPACK 3, were evaluated for reliability, robustness, accuracy, speed, compactness, portability and simplicity. All were found lacking in one or more areas. Modified versions of the EISPACK routines TRED3, TQLRAT, TINVIT and TRBAK3 performed somewhat better. Changes to TINVIT were especially important for improved speed, accuracy and reliability. To achieve the maximum capabilities of the FPS-X64 series of computers access to table memory is required, but since the FORTRAN compiler does not allow this and there is no library support for the required operations, it was necessary to write three routines in APAL. The standard algorithm needs to be modified before full efficiency can be achieved for the back transformation.