References
- Agullo, E., Demmel, J., Dongarra, J., Hadri, B., Kurzak, J., Langou, J., Ltaief, H., Luszczek, P. and Tomov, S. (2009). Numerical linear algebra on emerging architectures: The PLASMA and MAGMA projects, Journal of Physics: Conference Series180(1): 012037.
- Amdahl, G.M. (1967). Validity of the single processor approach to achieving large scale computing capabilities, Proceedings of the Spring Joint Computer Conference, AFIPS’67 (Spring), Atlantic City, NJ, USA, pp. 483–485.
- Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A. and Sorensen, D. (1999). LAPACK Users’ Guide, 3rd Edn., SIAM, Philadelphia, PA.
- Buttari, A., Langou, J., Kurzak, J. and Dongarra, J. (2009). A class of parallel tiled linear algebra algorithms for multicore architectures, Parallel Computing35(1): 38–53.
- Bylina, B. (2018). The block WZ factorization, Journal of Computational and Applied Mathematics331(C): 119–132.
- Bylina, B. and Bylina, J. (2007). Incomplete WZ factorization as an alternative method of preconditioning for solving Markov chains, in R. Wyrzykowski et al. (Eds.), PPAM, Lecture Notes in Computer Science, Vol. 4967, Springer, Berlin/Heidelberg, pp. 99–107.
- Bylina, B. and Bylina, J. (2009). Influence of preconditioning and blocking on accuracy in solving Markovian models, International Journal of Applied Mathematics and Computer Science19(2): 207–217, DOI: 10.2478/v10006-009-0017-3.10.2478/v10006-009-0017-3
- Bylina, B. and Bylina, J. (2015). Strategies of parallelizing nested loops on the multicore architectures on the example of the WZ factorization for the dense matrices, in M. Ganzha et al. (Eds.), Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, Annals of Computer Science and Information Systems, Vol. 5, IEEE, Piscataway, NJ, pp. 629–639.
- Donfack, S., Dongarra, J., Faverge, M., Gates, M., Kurzak, J., Luszczek, P. and Yamazaki, I. (2015). A survey of recent developments in parallel implementations of Gaussian elimination, Concurrency and Computation: Practice and Experience27(5): 1292–1309.
- Dongarra, J., DuCroz, J., Duff, I.S. and Hammarling, S. (1990). A set of level-3 basic linear algebra subprograms, ACM Transactions on Mathematics Software16(1): 1–17.
- Dongarra, J.J., Faverge, M., Ltaief, H. and Luszczek, P. (2013). Achieving numerical accuracy and high performance using recursive tile LU factorization, Concurrency and Computation: Practice and Experience26(6): 1408–1431.
- Dumas, J.G., Gautier, T., Pernet, C., Roch, J.L. and Sultan, Z. (2016). Recursion based parallelization of exact dense linear algebra routines for Gaussian elimination, Parallel Computing57: 235–249.
- Evans, D. and Hatzopoulos, M. (1979). A parallel linear system solver, International Journal of Computer Mathematics7(3): 227–238.
- Flynn, M.J. (1972). Some computer organizations and their effectiveness, IEEE Transactions on Computers21(9): 948–960.
- García, I., Merelo, J., Bruguera, J. and Zapata, E. (1990). Parallel quadrant interlocking factorization on hypercube computers, Parallel Computing15(1–3): 87–100.
- Gustavson, F.G. (1997). Recursion leads to automatic variable blocking for dense linear-algebra algorithms, IBM Journal of Research and Development41(6): 737–756.
- Intel (2019). Math Kernel Library, https://software.intel.com/en-us/mkl.
- Kurzak, J., Langou, J., Langou, C.D.J., Ltaief, H., Luszczek, P., Yarkhan, A., Haidar, A., Hoffman, J., Agullo, P.D.E., Buttari, A. and Hadri, B. (2010). PLASMA Users’ Guide: Parallel Linear Algebra Software for Multicore Architectures, Version 2.3., http://icl.cs.utk.edu/projectsfiles/plasma/pdf/users_guide.pdf.
- Marqués, M., Quintana-Ortí, G., Quintana-Ortí, E.S. and van de Geijn, R.A. (2011). Using desktop computers to solve large-scale dense linear algebra problems, The Journal of Supercomputing58(2): 145–150.
- Rao, S.C.S. (1997). Existence and uniqueness of WZ factorization, Parallel Computing23(8): 1129–1139.
- Yalamov, P. and Evans, D. (1995). The WZ matrix factorisation method, Parallel Computing21(7): 1111–1120.
- Yarkhan, A., Kurzak, J., Luszczek, P. and Dongarra, J. (2017). Porting the PLASMA numerical library to the OpenMP standard, International Journal of Parallel Programming45(3): 612–633, DOI:10.1007/s10766-016-0441-6.10.1007/s10766-016-0441-6