@article {,
	title = {Sparse matrix-vector and matrix-multivector products for the truncated SVD on graphics processors},
	journal = {Concurrency and Computation: Practice and Experience},
	year = {2023},
	month = {2023-08},
	abstract = {Many practical algorithms for numerical rank computations implement an iterative procedure that involves repeated multiplications of a vector, or a collection of vectors, with both a sparse matrix A and its transpose. Unfortunately, the realization of these sparse products on current high performance libraries often deliver much lower arithmetic throughput when the matrix involved in the product is transposed. In this work, we propose a hybrid sparse matrix layout, named CSRC, that combines the flexibility of some well-known sparse formats to offer a number of appealing properties: (1) CSRC can be obtained at low cost from the popular CSR (compressed sparse row) format; (2) CSRC has similar storage requirements as CSR; and especially, (3) the implementation of the sparse product kernels delivers high performance for both the direct product and its transposed variant on modern graphics accelerators thanks to a significant reduction of atomic operations compared to a conventional implementation based on CSR. This solution thus renders considerably higher performance when integrated into an iterative algorithm for the truncated singular value decomposition (SVD), such as the randomized SVD or, as demonstrated in the experimental results, the block Golub{\textendash}Kahan{\textendash}Lanczos algorithm.},
	keywords = {graphics processing units, Singular value decomposition, sparse matrix-multivector product, sparse matrix-vector product},
	issn = {1532-0626},
	doi = {10.1002/cpe.7871},
	url = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/cpe.7871},
	author = {Jos{\'e} I. Aliaga and Hartwig Anzt and Enrique S. Quintana-Orti and Andres E. Thomas}
}
@conference {1160,
	title = {Variable-Size Batched LU for Small Matrices and Its Integration into Block-Jacobi Preconditioning},
	booktitle = {46th International Conference on Parallel Processing (ICPP)},
	year = {2017},
	month = {2017-08},
	publisher = {IEEE},
	organization = {IEEE},
	address = {Bristol, United Kingdom},
	abstract = {We present a set of new batched CUDA kernels for the LU factorization of a large collection of independent problems of different size, and the subsequent triangular solves. All kernels heavily exploit the registers of the graphics processing unit (GPU) in order to deliver high performance for small problems. The development of these kernels is motivated by the need for tackling this embarrassingly parallel scenario in the context of block-Jacobi preconditioning that is relevant for the iterative solution of sparse linear systems.},
	keywords = {graphics processing units, Jacobian matrices, Kernel, linear systems, Parallel processing, Sparse matrices},
	doi = {10.1109/ICPP.2017.18},
	url = {http://ieeexplore.ieee.org/abstract/document/8025283/?reload=true},
	author = {Hartwig Anzt and Jack Dongarra and Goran Flegar and Enrique S. Quintana-Orti}
}
@inproceedings {992,
	title = {Efficiency of General Krylov Methods on GPUs {\textendash} An Experimental Study},
	journal = {2016 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)},
	year = {2016},
	month = {2016-05},
	pages = {683-691},
	abstract = {This paper compares different Krylov methods based on short recurrences with respect to their efficiency whenimplemented on GPUs. The comparison includes BiCGSTAB, CGS, QMR, and IDR using different shadow space dimensions. These methods are known for their good convergencecharacteristics. For a large set of test matrices taken from theUniversity of Florida Matrix Collection, we evaluate the methods{\textquoteright}performance against different target metrics: convergence, number of sparse matrix-vector multiplications, and executiontime. We also analyze whether the methods are "orthogonal"in terms of problem suitability. We propose best practicesfor choosing methods in a "black box" scenario, where noinformation about the optimal solver is available.},
	keywords = {algorithmic bombardment, BiCGSTAB, CGS, Convergence, Electric breakdown, gpu, graphics processing units, Hardware, IDR(s), Krylov solver, Libraries, linear systems, QMR, Sparse matrices},
	doi = {10.1109/IPDPSW.2016.45},
	author = {Hartwig Anzt and Jack Dongarra and Moritz Kreutzer and Gerhard Wellein and Martin Kohler}
}
@article {825,
	title = {Improving the Energy Efficiency of Sparse Linear System Solvers on Multicore and Manycore Systems},
	journal = {Philosophical Transactions of the Royal Society A -- Mathematical, Physical and Engineering Sciences},
	volume = {372},
	year = {2014},
	month = {2014-07},
	abstract = {While most recent breakthroughs in scientific research rely on complex simulations carried out in large-scale supercomputers, the power draft and energy spent for this purpose is increasingly becoming a limiting factor to this trend. In this paper, we provide an overview of the current status in energy-efficient scientific computing by reviewing different technologies used to monitor power draft as well as power- and energy-saving mechanisms available in commodity hardware. For the particular domain of sparse linear algebra, we analyze the energy efficiency of a broad collection of hardware architectures and investigate how algorithmic and implementation modifications can improve the energy performance of sparse linear system solvers, without negatively impacting their performance.},
	keywords = {energy efficiency, graphics processing units, High Performance Computing, iterative solvers, multicore processors, sparse linear systems},
	doi = {10.1098/rsta.2013.0279},
	author = {Hartwig Anzt and Enrique S. Quintana-Orti}
}
@article {icl:721,
	title = {Accelerating Linear System Solutions Using Randomization Techniques},
	journal = {ACM Transactions on Mathematical Software (also LAWN 246)},
	volume = {39},
	year = {2013},
	month = {2013-02},
	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.},
	keywords = {algorithms, dense linear algebra, experimentation, graphics processing units, linear systems, lu factorization, multiplicative preconditioning, numerical linear algebra, performance, plasma, randomization},
	doi = {10.1145/2427023.2427025},
	url = {http://dl.acm.org/citation.cfm?id=2427025},
	author = {Marc Baboulin and Jack Dongarra and Julien Herrmann and Stanimire Tomov}
}
