3 papers
math.NA2017
Discrete Energy Laws for the First-Order System Least-Squares Finite-Element Approach
J. H. Adler, I. Lashuk, S. P. MacLachlan +1
This paper analyzes the discrete energy laws associated with first-order system least-squares (FOSLS) discretizations of time-dependent partial differential equations. Using the he…
cs.MS2007
Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in hypre and PETSc
A. V. Knyazev, M. E. Argentati, I. Lashuk +1
We describe our software package Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) publicly released recently. BLOPEX is available as a stand-alone serial library, a…
math.NA2006
Steepest descent and conjugate gradient methods with variable preconditioning
Andrew V. Knyazev, Ilya Lashuk
We analyze the conjugate gradient (CG) method with variable preconditioning for solving a linear system with a real symmetric positive definite (SPD) matrix of coefficients . We…