We study the impact of non-uniform memory accesses (NUMA) on the solution of dense general linear systems using an LU factorization algorithm. In particular we illustrate how an appropriate placement of the threads and memory on a NUMA architecture can improve the performance of the panel factorization and consequently accelerate the global LU factorization. We apply these placement strategies ...

Systems of linear equations can be represented by matrix equations of the form A~x = ~b. LU Factorization is a method for solving systems in this form by transforming the matrix A into a form that makes backwards and forward susbstitution feasible. A common algorithm for LU factorization is Gaussian elimination, which I used for my serial and parallel implementations. I investigated using async...

Many of the currently popular \block algorithms" are scalar algorithms in which the operations have been grouped and reordered into matrix operations. One genuine block algorithm in practical use is block LU factorization, and this has recently been shown by Demmel and Higham to be unstable in general. It is shown here that block LU factorization is stable if A is block diagonally dominant by c...

We present the LU decomposition with panel rank revealing pivoting (LU PRRP), an LU factorization algorithm based on strong rank revealing QR panel factorization. LU PRRP is more stable than Gaussian elimination with partial pivoting (GEPP), with a theoretical upper bound of the growth factor of (1+ τb) n b , where b is the size of the panel used during the block factorization, τ is a parameter...

Many of the currently popular ‘block algorithms’ are scalar algorithms in which the operations have been grouped and reordered into matrix operations. One genuine block algorithm in practical use is block LU factorization, and this has recently been shown by Demmel and Higham to be unstable in general. It is shown here that block LU factorization is stable if A is block diagonally dominant by c...

In this technical report we study different parallel graph coloring algorithms and their application to the incomplete-LU factorization. We implement graph coloring based on different heuristics and showcase their performance on the GPU. We also present a comprehensive comparison of level-scheduling and graph coloring approaches for the incomplete-LU factorization and triangular solve. We discu...

The Multicore+GPU architecture has been adopted in some of the fastest supercomputers listed on the TOP500. The MAGMA project aims to develop a dense linear algebra library similar to LAPACK but for heterogeneous/hybrid architectures processors like Multicore+GPU. However, to provide portable performance, manual parameter tuning is required. This paper presents automatically tuned LU factorizat...