Supermatrix out-of-order scheduling of matrix operations for SMP and multi-core architectures
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
SuperMatrix: a multithreaded runtime scheduling system for algorithms-by-blocks
Proceedings of the 13th ACM SIGPLAN Symposium on Principles and practice of parallel programming
Benchmarking GPUs to tune dense linear algebra
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
Distributed SBP Cholesky factorization algorithms with near-optimal scheduling
ACM Transactions on Mathematical Software (TOMS)
Programming matrix algorithms-by-blocks for thread-level parallelism
ACM Transactions on Mathematical Software (TOMS)
Implementing linear algebra routines on multi-core processors with pipelining and a look ahead
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Parallel tiled QR factorization for multicore architectures
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
Scheduling two-sided transformations using tile algorithms on multicore architectures
Scientific Programming
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In many engineering applications, a solution of Fx = b is required, where F is a positive definite symmetric matrix. This is usually done by the Cholesky factorization, F = RRT, where R is the lower triangular Cholesky factor. This is a compute intensive problem. However, in order to achieve the best possible performance on IBM 3090 Vector Facility, the problem requires blocking at various levels to match 3090 memory hierarchy. A large problem which does not fit in a particular level of memory is blocked so that each block fits in memory. This minimizes data transfers between various levels of memory. In this paper, various blocking schemes are described for vector and parallel implementation on 3090 VF. Some of these algorithms have been included in the Engineering and Scientific Subroutine Library (ESSL). Performance numbers are also included. These algorithms achieve close to the peak performance of the 3090 uniprocessor and multiprocessors.