GPU acceleration of preconditioned solvers for ill-conditioned linear systems

In this work we study the implementations of deflation and preconditioning techniques for solving ill-conditioned linear systems using iterative methods. Solving such systems can be a time-consuming process because of the jumps in the coefficients due to large difference in material properties. We have developed implementations of the iterative...

Conjugate Gradients and Conjugate Residuals type methods for solving Least Squares problems from Tomography

This research investigates iterative methods for solving large and sparse least squares problems, as those encountered in tomography. A widely used method for such systems is the Conjugate Gradients method for Least Squares problems (CGLS), which is derived from the popular Conjugate Gradient method. The Conjugate Residuals method can also be...

A Comparison of Two-Level Preconditioners Based on Multigrid and Deflation

It is well known that two-level and multilevel preconditioned conjugate gradient (PCG) methods provide efficient techniques for solving large and sparse linear systems whose coefficient matrices are symmetric and positive definite. A two-level PCG method combines a traditional (one-level) preconditioner, such as incomplete Cholesky, with a...

Improving the linear solver used in the interactive wave model of a real-time ship simulator