Distributed orthogonal factorization: givens and householder algorithms
SIAM Journal on Scientific and Statistical Computing
LAPACK's user's guide
ScaLAPACK user's guide
Supercomputing '96 Proceedings of the 1996 ACM/IEEE conference on Supercomputing
Parallel tiled QR factorization for multicore architectures
Concurrency and Computation: Practice & Experience
Dynamic task scheduling for linear algebra algorithms on distributed-memory multicore systems
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
Distributed QR factorization based on randomized algorithms
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
A framework for low-communication 1-D FFT
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Hierarchical QR factorization algorithms for multi-core clusters
Parallel Computing
Tera-scale 1D FFT with low-communication algorithm and Intel® Xeon Phi™ coprocessors
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Scalable matrix decompositions with multiple cores on FPGAs
Microprocessors & Microsystems
A framework for low-communication 1-D FFT
Scientific Programming - Selected Papers from Super Computing 2012
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As tile linear algebra algorithms continue achieving high performance on shared-memory multicore architectures, it is a challenging task to make them scalable on distributed-memory multicore cluster machines. The main contribution of this paper is the extension to the distributed-memory environment of the previous work done by Hadri et al. on Communication- Avoiding QR (CA-QR) factorizations for tall and skinny matrices (initially done on shared-memory multicore systems). The fine granularity of tile algorithms associated with communicationavoiding techniques for the QR factorization presents a high degree of parallelism where multiple tasks can be concurrently executed, computation and communication largely overlapped, and computation steps fully pipelined. A decentralized dynamic scheduler has then been integrated as a runtime system to efficiently schedule tasks across the distributed resources. Our experimental results performed on two clusters (with dual-core and 8-core nodes, respectively) and a Cray XT5 system with 12-core nodes show that the tile CA-QR factorization is able to outperform the de facto ScaLAPACK library by up to 4 times for tall and skinny matrices, and has good scalability on up to 3,072 cores.