Using desktop computers to solve large-scale dense linear algebra problems

We provide experimental evidence that current desktop computers feature enough computational power to solve large-scale dense linear algebra problems. While the high computational cost of the numerical methods for solving these problems can be tackled by the multiple cores of current processors, we propose to use the disk to store the large data structures associated with these applications. Our results also show that the limited amount of RAM and the comparatively slow disk of the system pose no problem for the solution of very large dense linear systems and linear least-squares problems. Thus, current desktop computers are revealed as an appealing, cost-effective platform for research groups that have to deal with large dense linear algebra problems but have no direct access to large computing facilities.

[1]  Robert A. van de Geijn,et al.  Parallel out-of-core computation and updating of the QR factorization , 2005, TOMS.

[2]  Byron D. Tapley,et al.  Computational methods and processing strategies for estimating earth's gravity field , 2004 .

[3]  Robert A. van de Geijn,et al.  Solving “large” dense matrix problems on multi-core processors , 2009, 2009 IEEE International Symposium on Parallel & Distributed Processing.

[4]  Dan Negrut,et al.  Implicit Integration in Molecular Dynamics Simulation , 2008 .

[5]  Robert A. van de Geijn,et al.  Programming matrix algorithms-by-blocks for thread-level parallelism , 2009, TOMS.

[6]  J. T. Oden,et al.  Massively parallel computation for acoustical scattering problems using boundary element methods , 1996 .

[7]  Yu Zhang,et al.  Parallel MoM using higher order basis function and PLAPACK In-core and out-of-core solvers for challenging EM simulations , 2008, 2008 IEEE Antennas and Propagation Society International Symposium.

[8]  Marc Baboulin,et al.  Solving large dense linear least squares problems on parallel distributed computers. Application to the Earth's gravity field computation. , 2006 .

[9]  David S. Watkins,et al.  Fundamentals of Matrix Computations: Watkins/Fundamentals of Matrix Computations , 2005 .

[10]  David S. Watkins,et al.  Fundamentals of matrix computations , 1991 .

[11]  Robert A. van de Geijn,et al.  Parallel out-of-core cholesky and QR factorizations with POOCLAPACK , 2001, Proceedings 15th International Parallel and Distributed Processing Symposium. IPDPS 2001.

[12]  Robert A. van de Geijn,et al.  Rapid Development of High-Performance Out-of-Core Solvers , 2004, PARA.

[13]  Robert A. van de Geijn,et al.  Updating an LU Factorization with Pivoting , 2008, TOMS.

[14]  Robert A. van de Geijn,et al.  Out-of-Core Computation of the QR Factorization on Multi-core Processors , 2009, Euro-Par.