Gary W. Howell

Learn More
On cache based computer architectures using current standard algorithms, Householder bidiagonalization requires a significant portion of the execution time for computing matrix singular values and vectors. In this paper we reorganize the sequence of operations for Householder bidiagonalization of a general <i>m</i> &#215; <i>n</i> matrix, so that two(More)
BHESS uses Gaussian similarity transformations to reduce a general real square matrix to similar upper Hessenberg form. Multipliers are bounded in root mean square by a user-supplied parameter. If the input matrix is not highly nonnormal and the user-supplied tolerance on multipliers is of a size greater than ten, the returned matrix usually has small upper(More)
The BR algorithm, a new method for calculating the eigenvalues of an upper Hes-senberg matrix, is introduced. It is a bulge-chasing algorithm like the QR algorithm, but, unlike the QR algorithm, it is well adapted to computing the eigenvalues of the narrow-band, nearly tridiagonal matrices generated by the look-ahead Lanczos process. This paper describes(More)
This paper describes Householder reduction of a rectangular sparse matrix to small band upper triangular form B k+1. B k+1 is upper triangular with nonzero entries only on the diagonal and on the nearest k superdiagonals. The algorithm is similar to the Householder reduction used as part of the standard dense SVD computation. For the sparse " lazy "(More)
We investigate how to use an LU factorization with the classical lsqr routine for solving overdetermined sparse least squares problems. Usually L is much better conditioned than A and iterating with L instead of A results in faster convergence. When a runtime test indicates that L is not sufficiently well-conditioned, a partial orthogonalization of L(More)
ChemModLab, written by the ECCR @ NCSU consortium under NIH support, is a toolbox for fitting and assessing quantitative structure-activity relationships (QSARs). Its elements are: a cheminformatic front end used to supply molecular descriptors for use in modeling; a set of methods for fitting models; and methods for validating the resulting model.(More)