Rapid Development of High-Performance Out-of-Core Solvers

In this paper, we discuss a more scalable OOC implementation of a dense linear system solver via LU factorization that presents numerical stability similar to that of the LU factorization with partial pivoting. Our implementation builds on the Formal Linear Algebra Methods Environment (FLAME), the Parallel Linear Algebra Package (PLAPACK), and the Parallel Out-of-Core Linear Algebra Package (POOCLAPACK) infrastructures. Experimental results on an Intel Itanium2 (R) platform demonstrate the high performance of this approach.

[1]  Robert A. van de Geijn,et al.  FLAME: Formal Linear Algebra Methods Environment , 2001, TOMS.

[2]  Jack Dongarra,et al.  The design and implementation of the parallel out-of-core ScaLAPACK LU, QR and Cholesky factorization routines , 1997 .

[3]  Robert A. van de Geijn,et al.  Using PLAPACK - parallel linear algebra package , 1997 .

[4]  Gene H. Golub,et al.  Matrix computations , 1983 .

[5]  Jack Dongarra,et al.  The Design and Implementation of the Parallel Out-of-coreScaLAPACK LU, QR, and Cholesky Factorization Routines , 1997 .

[6]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[7]  James Demmel,et al.  LAPACK Users' Guide, Third Edition , 1999, Software, Environments and Tools.

[8]  Sivan Toledo Locality of Reference in LU Decomposition with Partial Pivoting , 1997, SIAM J. Matrix Anal. Appl..

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

[10]  Sivan Toledo,et al.  The design and implementation of SOLAR, a portable library for scalable out-of-core linear algebra computations , 1996, IOPADS '96.

[11]  Sivan Toledo,et al.  A survey of out-of-core algorithms in numerical linear algebra , 1999, External Memory Algorithms.

[12]  Robert A. van de Geijn,et al.  POOCLAPACK: Parallel Out-of-Core Linear Algebra Package , 1999 .

[13]  Jack Dongarra,et al.  ScaLAPACK Users' Guide , 1987 .

[14]  Tom Cwik,et al.  Application of massively parallel computation to integral equation models of electromagnetic scattering , 1994 .

[15]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

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

[17]  Jack Dongarra,et al.  LINPACK Users' Guide , 1987 .

[18]  L. Trefethen,et al.  Average-case stability of Gaussian elimination , 1990 .

[19]  Robert A. van de Geijn,et al.  The science of deriving dense linear algebra algorithms , 2005, TOMS.

[20]  Bo Kågström,et al.  GEMM-based level 3 BLAS: high-performance model implementations and performance evaluation benchmark , 1998, TOMS.