@article {1219,
	title = {Optimization and Performance Evaluation of the IDR Iterative Krylov Solver on GPUs},
	journal = {The International Journal of High Performance Computing Applications},
	volume = {32},
	number = {2},
	year = {2018},
	month = {2018-03},
	pages = {220{\textendash}230},
	abstract = {In this paper, we present an optimized GPU implementation for the induced dimension reduction algorithm. We improve data locality, combine it with an efficient sparse matrix vector kernel, and investigate the potential of overlapping computation with communication as well as the possibility of concurrent kernel execution. A comprehensive performance evaluation is conducted using a suitable performance model. The analysis reveals efficiency of up to 90\%, which indicates that the implementation achieves performance close to the theoretically attainable bound.},
	keywords = {co-design, gpu, Induced dimension reduction (IDR), kernel fusion, kernel overlap, roofline performance model},
	doi = {https://doi.org/10.1177/1094342016646844},
	author = {Hartwig Anzt and Moritz Kreutzer and Eduardo Ponce and Gregory D. Peterson and Gerhard Wellein and Jack Dongarra}
}
@article {1067,
	title = {Preconditioned Krylov Solvers on GPUs},
	journal = {Parallel Computing},
	year = {2017},
	month = {2017-06},
	abstract = {In this paper, we study the effect of enhancing GPU-accelerated Krylov solvers with preconditioners. We consider the BiCGSTAB, CGS, QMR, and IDR(s) Krylov solvers. For a large set of test matrices, we assess the impact of Jacobi and incomplete factorization preconditioning on the solvers{\textquoteright} numerical stability and time-to-solution performance. We also analyze how the use of a preconditioner impacts the choice of the fastest solver.},
	keywords = {gpu, ILU, Jacobi, Krylov solvers, Preconditioning},
	issn = {01678191},
	doi = {10.1016/j.parco.2017.05.006},
	url = {http://www.sciencedirect.com/science/article/pii/S0167819117300777},
	author = {Hartwig Anzt and Mark Gates and Jack Dongarra and Moritz Kreutzer and Gerhard Wellein and Martin Kohler}
}
@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}
}
@conference {937,
	title = {Efficiency of General Krylov Methods on GPUs {\textendash} An Experimental Study},
	booktitle = {The Sixth International Workshop on Accelerators and Hybrid Exascale Systems (AsHES)},
	year = {2016},
	month = {2016-05},
	publisher = {IEEE},
	organization = {IEEE},
	address = {Chicago, IL},
	abstract = {This paper compares different Krylov methods based on short recurrences with respect to their efficiency when implemented on GPUs. The comparison includes BiCGSTAB, CGS, QMR, and IDR using different shadow space dimensions. These methods are known for their good convergence characteristics. For a large set of test matrices taken from the University of Florida Matrix Collection, we evaluate the methods{\textquoteright}
performance against different target metrics: convergence, number of sparse matrix-vector multiplications, and execution time. We also analyze whether the methods are {\textquotedblleft}orthogonal{\textquotedblright} in terms of problem suitability. We propose best practices for choosing methods in a {\textquotedblleft}black box{\textquotedblright} scenario, where no information about the optimal solver is available.},
	keywords = {algorithmic bombardment, BiCGSTAB, CGS, gpu, IDR(s), Krylov solver, QMR},
	doi = {10.1109/IPDPSW.2016.45},
	author = {Hartwig Anzt and Jack Dongarra and Moritz Kreutzer and Gerhard Wellein and Martin Kohler}
}
