CALU: A Communication Optimal LU Factorization Algorithm

CALU: A Communication Optimal LU Factorization Algorithm

Since the cost of communication (moving data) greatly exceeds the cost of doing arithmetic on current and future computing platforms, we are motivated to devise algorithms that communicate as little as possible, even if they do slightly more arithmetic, and as long as they still get the right answer. This paper is about getting the right answer for such an algorithm. It discusses CALU, a commun...

LU-AD1 Factorization Algorithm

Communication-Optimal Parallel 2.5D Matrix Multiplication and LU Factorization Algorithms

Extra memory allows parallel matrix multiplication to be done with asymptotically less communication than Cannon’s algorithm and be faster in practice. “3D” algorithms arrange the p processors in a 3D array, and store redundant copies of the matrices on each of p layers. ‘2D” algorithms such as Cannon’s algorithm store a single copy of the matrices on a 2D array of processors. We generalize the...

Avoiding Communication through a Multilevel LU Factorization

Due to the evolution of massively parallel computers towards deeper levels of parallelism and memory hierarchy, and due to the exponentially increasing ratio of the time required to transfer data, either through the memory hierarchy or between different compute units, to the time required to compute floating point operations, the algorithms are confronted with two challenges. They need not only...

The Gauss-Huard algorithm and LU factorization

In this paper we analyze the Gauss-Huard algorithm. From a description of the algorithm in terms of matrix-vector operations we reveal a close relation between the Gauss-Huard algorithm and an LU factorization as constructed in an ikj variant.