The matrix-form LSQR method is presented in this paper for solving the least squares problem of the matrix equation AXB = C with tridiagonal matrix constraint. Based on a matrix-form bidiagonalization procedure, the least squares problem associated with the tridiagonal constrained matrix equation AXB = C reduces to a unconstrained least squares problem of linear system, which can be solved by u...

The irlba package provides a fast way to compute partial singular value decompositions (SVD) of large sparse or dense matrices. Recent additions to the package can also compute fast partial symmetric eigenvalue decompositions and principal components. The package is an R implementation of the augmented implicitly restarted Lanczos bidiagonalization algorithm of Jim Baglama and Lothar Reichel. S...

Two new algorithms for one-sided bidiagonalization are presented. The first is a block version which improves execution time by improving cache utilization from the use of BLAS 2.5 operations and more BLAS 3 operations. The second is adapted to parallel computation. When incorporated into singular value decomposition software, the second algorithm is faster than the corresponding ScaLAPACK rout...

Jacobi matrices are parametrized by their eigenvalues and norming constants (first coordinates of normalized eigenvectors): this coordinate system breaks down at reducible tridiagonal matrices. The set of real symmetric tridiagonal matrices with prescribed simple spectrum is a compact manifold, admitting an open covering by open dense sets Uπ Λ centered at diagonal matrices Λπ , where π spans t...

The L-curve is often applied to determine a suitable value of the regularization parameter when solving ill-conditioned linear systems of equations with a right-hand side contaminated by errors of unknown norm. The location of the vertex of the L-curve typically yields a suitable value of the regularization parameter. However, the computation of the L-curve and of its curvature is quite costly ...

Abstract We discuss the singularity structure of Kahan discretizations a class quadratic vector fields and provide classification parameter values such that corresponding map is integrable, in particular, admits an invariant pencil elliptic curves.

The generalized null space decomposition (GNSD) is a unitary reduction of a general matrix A of order n to a block upper triangular form that reveals the structure of the Jordan blocks of A corresponding to a zero eigenvalue. The reduction was introduced by Kublanovskaya. It was extended first by Ruhe and then by Golub and Wilkinson, who based the reduction on the singular value decomposition. ...

Title of Dissertation: EMPIRICAL STUDIES IN PARALLEL SORTING Evan Golub, Doctor of Philosophy, 1999 Dissertation Directed By: Professor William Gasarch, Associate Professor Clyde Kruskal, Department of Computer Science I examine different parallel algorithms for sorting in rounds. Most of these algorithms use a graph to indicate the comparisons to be made. The primary difference between the alg...