Electromagnetic scattering calculations on the Intel Touchstone Delta
Proceedings of the 1992 ACM/IEEE conference on Supercomputing
Factoring Symmetric Indefinite Matrices on High-Performance Architectures
SIAM Journal on Matrix Analysis and Applications
Proceedings of the fourth workshop on I/O in parallel and distributed systems: part of the federated computing research conference
Accurate Symmetric Indefinite Linear Equation Solvers
SIAM Journal on Matrix Analysis and Applications
Scalable parallel algorithms for surface fitting and data mining
Parallel Computing - Linear systems and associated problems
Parallel Out-of-Core Cholesky and QR Factorization with POOCLAPACK
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
Frequency Interpolation Methods for Accelerating Parallel EMCAnalysis
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
Evaluating Block Algorithm Variants in LAPACK
Proceedings of the Fourth SIAM Conference on Parallel Processing for Scientific Computing
Key Concepts for Parallel Out-Of-Core LU Factorization
Key Concepts for Parallel Out-Of-Core LU Factorization
On the performance of parallel factorization of out-of-core matrices
Parallel Computing
Reducing the amount of pivoting in symmetric indefinite systems
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
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In the factorization of indefinite symmetric linear systems, symmetric pivoting is required to maintain numerical stability, while attaining a reduced floating point operation count. However, symmetric pivoting presents many challenges in the design of efficient algorithms, and especially in the context of a parallel out-of core solver for dense systems. Here, the search for a candidate pivot in order to eliminate a single column potentially requires a large number of messages and accesses of disk blocks. In this paper, we look at the problems of scalability in terms of number of processors and the ratio of data size relative to aggregate memory capacity for these solvers. We find that diagonal pivoting methods which exploit locality of pivots offer the best potential to meet these demands. A left-looking algorithm based on an exhaustive block-search strategy for dense matrices is described and analysed; its scalability in terms of parallel I/O is dependent on being able to find stable pivots near or within the current elimination block.