Assignment:

1. Possibility I: Sparse matrix-vector multiplication in parallel
   Make a discussion regarding methods to implement sparse matrix-vector multiplication in parallel - advantages and disadvantages, related to some computer architecture (cluster, cluster with an accelerator, GPU). This should be done in a written form, based on experience, published in one or more articles on the topic. Some articles are given below.
   Note: You are not expected to review all the articles. Make a relevant choice. You are welcome to find other sources with the requirement that these are published recently and are of relevance for the current computer architectures.

   Some references:

   • Ariful Azad, Aydin Buluc, A work-efficient parallel sparse matrix-sparse vector multiplication algorithm, IEEE International Parallel & Distributed Processing Symposium (IPDPS), Orlando, FL, May 2017, here
   • S. Williams, L. Oliker, R. Vuduc, J. Shalf, K. Yelick, J. Demmel, "Optimization of Sparse Matrix-Vector Multiplication on Emerging Multicore Platforms", Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis (SC), November 2007, here
   • S. Williams, N. Bell, J. W. Choi, M. Garland, L. Oliker, R. Vuduc, "Sparse Matrix-Vector Multiplication on Multicore and Accelerators", chapter in Scientific Computing with Multicore and Accelerators, edited by Jack Dongarra, David A. Bader, Jakub Kurzak, ( 2010)
   • L. Lin, J. Lu and L. Ying, "Fast construction of hierarchical matrix representation from matrix-vector multiplication", J. Comput. Phys., 2011, 230:4071,
   • A. Buluç, S. Williams, L. Oliker, J. Demmel, "Reduced-Bandwidth Multithreaded Algorithms for Sparse Matrix-Vector Multiplication", International Parallel Distributed Processing Symposium (IPDPS), May 2011, doi: 10.1109/IPDPS.2011.73
   • D. Oryspayev, P. Maris, J. P. Vary, M. Sosonkina, H. M. Aktulga, "A Memory-efficient Scalable Symmetric Sparse Matrix Vector Multiplication Algorithm for Distributed Memory Architectures", Concurrency and Computation: Practice and Experience, March 8, 2014,

2. Possibility II: Benchmarking pipelined preconditioned iterative methods
   Implement in Matlab the pipelined preconditioned versions of CG and GMRES, following [A].
   Test the methods against the same methods available in Matlab regarding convergence (do you get the same number of iterations) and time. As a preconditioner, use some incomplete factorization preconditioner (ichol, ilu). Seek a couple of interesting matrices, spd and nonsymmetric, say from matrix market.
   Test Matlab's parfor around the vector updates in the pipelined CG and GMRES to see whether you get an improved performance.
   Write a short report on the results and the possible potential for performance improvement.

   [A] P. Sanan, S.M. Schnepp, D.A. May, Pipelined flexible Krylov subspace methods (Ref [3] at the course description page).

3. Possibility III: Suggest your own project, which could be beneficial for your research.