Abstract
We illustrate how linear algebra calculations can be enhanced by statistical techniques in the case of a square linear system Ax = b. We study a random transformation of A that enables us to avoid pivoting and then to reduce the amount of communication. Numerical experiments show that this randomization can be performed at a very affordable computational price while providing us with a satisfying accuracy when compared to partial pivoting. This random transformation called Partial Random Butterfly Transformation (PRBT) is optimized in terms of data storage and flops count. We propose a solver where PRBT and the LU factorization with no pivoting take advantage of the current hybrid multicore/GPU machines and we compare its Gflop/s performance with a solver implemented in a current parallel library.
Original language | English |
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Article number | 8 |
Journal | ACM Transactions on Mathematical Software |
Volume | 39 |
Issue number | 2 |
DOIs | |
State | Published - Feb 2013 |
Keywords
- Dense linear algebra
- Graphics processing units
- LU factorization
- Linear systems
- Multiplicative preconditioning
- Randomization