Solving a sparse system using linear algebra

Certified sparse linear system solving

Solving Alignment Using Elementary Linear Algebra

Data and computation alignment is an important part of compiling sequential programs to architectures with non uniform memory access times In this paper we show that elementary matrix methods can be used to determine communication free alignment of code and data We also solve the problem of replicating data to eliminate communication Our matrix based approach leads to algorithms which work well...

Nearly Sparse Linear Algebra

In this article, we propose a method to perform linear algebra on a matrix with nearly sparse properties. More precisely, although we require the main part of the matrix to be sparse, we allow some dense columns with possibly large coefficients. We modify Block Wiedemann algorithm and show that the contribution of these heavy columns can be made negligible compared to the one of the sparse part...

Solving Sparse Linear Constraints

Linear arithmetic decision procedures form an important part of theorem provers for program verification. In most verification benchmarks, the linear arithmetic constraints are dominated by simple difference constraints of the form x ≤ y + c. Sparse linear arithmetic (SLA) denotes a set of linear arithmetic constraints with a very few non-difference constraints. In this paper, we propose an eff...

Sparse linear algebra on a GPU

We investigate what the graphics processing units (GPUs) have to offer compared to the central processing units (CPUs) when solving a sparse linear system of equations. This is performed by using a GPU to simulate fluid-flow in a porous medium. Flow-problems are discretized mainly by the mimetic finite element discretization, but also by a two-point fluxapproximation (TPFA) method. Both of thes...