@article {936,
	title = {Parallel Programming Models for Dense Linear Algebra on Heterogeneous Systems},
	journal = {Supercomputing Frontiers and Innovations},
	volume = {2},
	number = {4},
	year = {2015},
	month = {2015-10},
	abstract = {We present a review of the current best practices in parallel programming models for dense linear algebra (DLA) on heterogeneous architectures. We consider multicore CPUs, stand alone manycore coprocessors, GPUs, and combinations of these. Of interest is the evolution of the programming models for DLA libraries {\textendash} in particular, the evolution from the popular LAPACK and ScaLAPACK libraries to their modernized counterparts PLASMA (for multicore CPUs) and MAGMA (for heterogeneous architectures), as well as other programming models and libraries. Besides providing insights into the programming techniques of the libraries considered, we outline our view of the current strengths and weaknesses of their programming models {\textendash} especially in regards to hardware trends and ease of programming high-performance numerical software that current applications need {\textendash} in order to motivate work and future directions for the next generation of parallel programming models for high-performance linear algebra libraries on heterogeneous systems.},
	keywords = {dense linear algebra, gpu, HPC, Multicore, plasma, Programming models, runtime},
	doi = {10.14529/jsfi1504},
	author = {Maksims Abalenkovs and Ahmad Abdelfattah and Jack Dongarra and Mark Gates and Azzam Haidar and Jakub Kurzak and Piotr Luszczek and Stanimire Tomov and Ichitaro Yamazaki and Asim YarKhan}
}
@article {699,
	title = {A Survey of Recent Developments in Parallel Implementations of Gaussian Elimination},
	journal = {Concurrency and Computation: Practice and Experience},
	volume = {27},
	year = {2015},
	month = {2015-04},
	pages = {1292-1309},
	abstract = {Gaussian elimination is a canonical linear algebra procedure for solving linear systems of equations. In the last few years, the algorithm has received a lot of attention in an attempt to improve its parallel performance. This article surveys recent developments in parallel implementations of Gaussian elimination for shared memory architecture. Five different flavors are investigated. Three of them are based on different strategies for pivoting: partial pivoting, incremental pivoting, and tournament pivoting. The fourth one replaces pivoting with the Partial Random Butterfly Transformation, and finally, an implementation without pivoting is used as a performance baseline. The technique of iterative refinement is applied to recover numerical accuracy when necessary. All parallel implementations are produced using dynamic, superscalar, runtime scheduling and tile matrix layout. Results on two multisocket multicore systems are presented. Performance and numerical accuracy is analyzed.},
	keywords = {Gaussian elimination, lu factorization, Multicore, parallel, plasma, shared memory},
	doi = {10.1002/cpe.3306},
	author = {Simplice Donfack and Jack Dongarra and Mathieu Faverge and Mark Gates and Jakub Kurzak and Piotr Luszczek and Ichitaro Yamazaki}
}
@article {icl:693,
	title = {LU Factorization with Partial Pivoting for a Multicore System with Accelerators},
	journal = {IEEE Transactions on Parallel and Distributed Computing},
	volume = {24},
	year = {2013},
	month = {2013-08},
	pages = {1613-1621},
	chapter = {1613},
	abstract = {LU factorization with partial pivoting is a canonical numerical procedure and the main component of the high performance LINPACK benchmark. This paper presents an implementation of the algorithm for a hybrid, shared memory, system with standard CPU cores and GPU accelerators. The difficulty of implementing the algorithm for such a system lies in the disproportion between the computational power of the CPUs, compared to the GPUs, and in the meager bandwidth of the communication link between their memory systems. An additional challenge comes from the complexity of the memory-bound and synchronization-rich nature of the panel factorization component of the block LU algorithm, imposed by the use of partial pivoting. The challenges are tackled with the use of a data layout geared toward complex memory hierarchies, autotuning of GPU kernels, fine-grain parallelization of memory-bound CPU operations and dynamic scheduling of tasks to different devices. Performance in excess of one TeraFLOPS is achieved using four AMD Magny Cours CPUs and four NVIDIA Fermi GPUs.},
	keywords = {accelerator, Gaussian elimination, gpu, lu factorization, manycore, Multicore, partial pivoting, plasma},
	doi = {http://doi.ieeecomputersociety.org/10.1109/TPDS.2012.242},
	author = {Jakub Kurzak and Piotr Luszczek and Jack Dongarra}
}
