66 citations · 115 across the 13 of their papers we have counts for
5 papers · 1 filter
Operator Coefficient Methods for Linear Equations
Joseph F. Grcar
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds o…
Matrix Stretching for Linear Equations
Joseph F. Grcar
Stretching is a new sparse matrix method that makes matrices sparser by making them larger. Stretching has implications for computational complexity theory and applications in scie…
Unattainability of A Perturbation Bound for Indefinite Linear Least Squares Problems
Joseph F. Grcar
Contrary to an assumption made by Bojanczyk, Higham, and Patel [SIAM J. Matrix Anal. Appl., 24(4):914-931, 2003], a perturbation bound for indefinite least square problems is capab…
Spectral Condition Numbers of Orthogonal Projections and Full Rank Linear Least Squares Residuals
Joseph F. Grcar
A simple formula is proved to be a tight estimate for the condition number of the full rank linear least squares residual with respect to the matrix of least squares coefficients a…
Nuclear Norms of Rank 2 Matrices for Spectral Condition Numbers of Full Rank Linear Least Squares Solutions
Joseph F. Grcar
The condition number of solutions to full rank linear least-squares problem are shown to be given by an optimization problem that involves nuclear norms of rank 2 matrices. The con…