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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> × <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)

- G. A. GEIST, G. W. HOWELL
- 1999

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)

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)

This note explores sparse matrix dense matrix (SMDM) multiplications , useful in block Krylov or block Lanczos methods. SMDM computations are AU , and V A, multiplication of a large sparse matrix m × n matrix A by a matrix V of k rows of length m or a matrix U of k columns of length k, k << m, k << n. In a block Lanc-zos or Krylov algorithm, matrix matrix… (More)

This paper introduces block Householder reduction of a rectangular sparse matrix to small band upper triangular form. The computation accesses a sparse matrix only for sparse matrix dense matrix (SMDM) multiplications and for "just in time" extractions of row and column blocks. For a bandwidth of <i>k</i> + 1, the dense matrices are the <i>k</i> rows or… (More)