[Ahmed, N., Mateev, N. and Pingali, K. (2000). Tiling imperfectly-nested loop nests, ACM/IEEE 2000 Conference on Supercomputing, Dallas, TX, USA, Article No. 31.]Search in Google Scholar
[Andonov, R., Balev, S., Rajopadhye, S. and Yanev, N. (2001). Optimal semi-oblique tiling, IEEE Transactions on Parallel and Distributed Systems 14(9): 940-966.10.1109/TPDS.2003.1233716]Search in Google Scholar
[Bastoul, C. (2004). Code generation in the polyhedral model is easier than you think, PACT’13, IEEE International Conference on Parallel Architecture and Compilation Techniques, Juan-les-Pins, France, pp. 7-16.]Search in Google Scholar
[Bastoul, C. and Feautrier, P. (2003). Improving data locality by chunking, International Conference on Compiler Construction, Warsaw, Poland, pp. 320-335.]Search in Google Scholar
[Beletska, A., Bielecki, W., Cohen, A., Palkowski, M. and Siedlecki, K. (2011). Coarse-grained loop parallelization: Iteration space slicing vs affine transformations, Parallel Computing 37(8): 479-497.10.1016/j.parco.2010.12.005]Search in Google Scholar
[Bielecki, W., Kraska, K. and Klimek, T. (2014). Using basis dependence distance vectors to calculate the transitive closure of dependence relations by means of the Floyd-Warshall algorithm, Journal of Combinatorial Optimization 30(2): 253-275.10.1007/s10878-014-9740-2]Search in Google Scholar
[Bielecki,W., Klimek, T., Palkowski, M. and Beletska, A. (2010). An iterative algorithm of computing the transitive closure of a union of parameterized affine integer tuple relations, in W. Wu and O. Daescu (Eds.), COCOA 2010: Fourth International Conference on Combinatorial Optimization and Applications, Lecture Notes in Computer Science, Vol. 6508, Springer, Berlin/Heidelberg, pp. 104-113.]Search in Google Scholar
[Bielecki, W. and Palkowski, M. (2015). Perfectly nested loop tiling transformations based on the transitive closure of the program dependence graph, in A. Wilinski et al. (Eds.), Soft Computing in Computer and Information Science, Advances in Intelligent Systems and Computing, Vol. 342, Springer International Publishing, Cham, pp. 309-320.10.1007/978-3-319-15147-2_26]Search in Google Scholar
[Bielecki, W., Palkowski, M. and Klimek, T. (2012). Free scheduling for statement instances of parameterized arbitrarily nested affine loops, Parallel Computing 38(9): 518-532.10.1016/j.parco.2012.06.001]Search in Google Scholar
[Bielecki, W., Palkowski, M. and Klimek, T. (2015). Free scheduling of tiles based on the transitive closure of dependence graphs, in R. Wyrzykowski (Ed.), 11th International Conference on Parallel Processing and Applied Mathematics, Part II, Lecture Notes in Computer Science, Vol. 9574, Springer, Berlin/Heidelberg, pp. 133-142.]Search in Google Scholar
[Błaszczyk, J., Karbowski, A. and Malinowski, K. (2007). Object library of algorithms for dynamic optimization problems: Benchmarking SQP and nonlinear interior point methods, International Journal of Applied Mathematics and Computer Science 17(4): 515-537, DOI: 10.2478/v10006-007-0043-y.10.2478/v10006-007-0043-y]Search in Google Scholar
[Bondhugula, U., Baskaran, M., Krishnamoorthy, S., Ramanujam, J., Rountev, A. and Sadayappan, P. (2008a). Automatic transformations for communication-minimized parallelization and locality optimization in the polyhedral model, in L. Hendren (Ed.), Compiler Constructure, Lecture Notes in Computer Science, Vol. 4959, Springer, Berlin/Heidelberg, pp. 132-146.]Search in Google Scholar
[Bondhugula, U., Hartono, A., Ramanujam, J. and Sadayappan, P. (2008b). A practical automatic polyhedral parallelizer and locality optimizer, ACM SIGPLAN Notices 43(6): 101-113.10.1145/1379022.1375595]Search in Google Scholar
[Campbell, S.L. (2001). Numerical analysis and systems theory, International Journal of Applied Mathematics and Computer Science 11(5): 1025-1034.]Search in Google Scholar
[Feautrier, P. (1992a). Some efficient solutions to the affine scheduling problem, I: One-dimensional time, International Journal of Parallel Programming 21(5): 313-348.10.1007/BF01407835]Search in Google Scholar
[Feautrier, P. (1992b). Some efficient solutions to the affine scheduling problem, II: Multidimensional time, International Journal of Parallel Programming 21(6): 389-420.10.1007/BF01379404]Search in Google Scholar
[Gan, G., Wang, X., Manzano, J. and Gao, G.R. (2009). Tile reduction: The first step towards tile aware parallelization in openmp, in M.S. Muller et al. (Eds.), Evolving OpenMP in an Age of Extreme Parallelism, Springer, Berlin/Heidelberg, pp. 140-153.10.1007/978-3-642-02303-3_12]Search in Google Scholar
[Greenbaum, A. and Chartier, T.P. (2012). Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms, Princeton University Press, Princeton, NJ.]Search in Google Scholar
[Griebl, M. (2004). Automatic Parallelization of Loop Programs for Distributed Memory Architectures, D.Sc. thesis, University of Passau, Passau.]Search in Google Scholar
[Griebl, M., Feautrier, P. and Lengauer, C. (2000). Index set splitting, International Journal of Parallel Programming 28(6): 607-631.10.1023/A:1007516818651]Search in Google Scholar
[Grosser, T., Cohen, A., Kelly, P.H., Ramanujam, J., Sadayappan, P. and Verdoolaege, S. (2013). Split tiling for GPUS: Automatic parallelization using trapezoidal tiles, Proceedings of the 6th Workshop on General Purpose Processor Using Graphics Processing Units, Houston, TX, USA, pp. 24-31.]Search in Google Scholar
[Irigoin, F. and Triolet, R. (1988). Supernode partitioning, Proceedings of the 15th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL’88, San Diego, CA, USA, pp. 319-329.]Search in Google Scholar
[Jeffers, J. and Reinders, J. (2015). High Performance Parallelism Pearls, Volume Two: Multicore and Many-Core Programming Approaches, Morgan Kaufmann, Burlington, MA.]Search in Google Scholar
[Kelly, W., Maslov, V., Pugh, W., Rosser, E., Shpeisman, T. and Wonnacott, D. (1995). The omega library interface guide, Technical report, University of Maryland at College Park, MD.]Search in Google Scholar
[Kelly, W., Pugh, W., Rosser, E. and Shpeisman, T. (1996). Transitive closure of infinite graphs and its applications, International Journal of Parallel Programming 24(6): 579-598.10.1007/BF03356760]Search in Google Scholar
[Kim, D. and Rajopadhye, S.V. (2009). Parameterized tiling for imperfectly nested loops, Technical Report CS-09-101, Colorado State University, Fort Collins, CO.]Search in Google Scholar
[Kowarschik, M. and Weiß, C. (2003). An overview of cache optimization techniques and cache-aware numerical algorithms, in U. Meyer et al. (Eds.), Algorithms for Memory Hierarchies, Springer, Berlin/Heidelberg, pp. 213-232.10.1007/3-540-36574-5_10]Search in Google Scholar
[Leader, J.J. (2004). Numerical Analysis and Scientific Computation, Pearson Addison/Wesley Boston, MA.]Search in Google Scholar
[Lim, A., Cheong, G.I. and Lam, M.S. (1999). An affine partitioning algorithm to maximize parallelism and minimize communication, Proceedings of the 13th ACM SIGARCH International Conference on Supercomputing, Rhodes, Greece, pp. 228-237.]Search in Google Scholar
[Lim, A.W. and Lam, M.S. (1994). Communication-free parallelization via affine transformations, in K. Pingali et al. (Eds.), 24th ACM Symposium on Principles of Programming Languages, Springer-Verlag, Berlin/Heidelberg, pp. 92-106.]Search in Google Scholar
[Maciążek, M., Grabowski, D. and Pasko,M. (2015). Genetic and combinatorial algorithms for optimal sizing and placement of active power filters, International Journal of Applied Mathematics and Computer Science 25(2): 269-279, DOI: 10.1515/amcs-2015-0021.10.1515/amcs-2015-0021]Search in Google Scholar
[McMahon, F.H. (1986). The Livermore Fortran kernels: A computer test of the numerical performance range, Technical Report UCRL-53745, Lawrence Livermore National Laboratory, Livermore, CA.]Search in Google Scholar
[Mullapudi, R.T. and Bondhugula, U. (2014). Tiling for dynamic scheduling, IMPACT 2014, 14th International Workshop on Polyhedral Compilation Techniques, Vienna, Austria.]Search in Google Scholar
[NAS (2015). NAS benchmarks suite, http://www.nas.nasa.gov.]Search in Google Scholar
[OpenMP Architecture Review Board (2012). OpenMP application program interface version 4.0, http:// www.openmp.org/mp-documents/OpenMP4.0RC1_final.pdf.]Search in Google Scholar
[Palkowski, M., Klimek, T. and Bielecki,W. (2015). TRACO: An automatic loop nest parallelizer for numerical applications, Federated Conference on Computer Science and Information Systems, Łódź, Poland, pp. 681-686]Search in Google Scholar
[Pol (2012). The Polyhedral benchmark suite, http://www.cse.ohio-state.edu/~pouchet/software/polybench/.]Search in Google Scholar
[Pugh, W. and Rosser, E. (1997). Iteration space slicing and its application to communication optimization, International Conference on Supercomputing, Vienna, Austria, pp. 221-228.]Search in Google Scholar
[Pugh, W. and Rosser, E. (1999). Iteration space slicing for locality, in L. Carter and J. Ferrante (Eds.), Languages and Compilers for Parallel Computing, Lecture Notes in Computer Science, Vol. 1863, Springer, Berlin/Heidelberg, pp. 164-184.]Search in Google Scholar
[Pugh, W. and Wonnacott, D. (1993). An exact method for analysis of value-based array data dependences, 6th Annual Workshop on Programming Languages and Compilers for Parallel Computing, Portland, OR, USA, pp. 546-566.]Search in Google Scholar
[Pugh, W. and Wonnacott, D. (1994). Static analysis of upper and lower bounds on dependences and parallelism, ACM Transactions on Programming Languages and Systems 16(4): 1248-1278.10.1145/183432.183525]Search in Google Scholar
[Ramanujam, J. and Sadayappan, P. (1992). Tiling multidimensional iteration spaces for multicomputers, Journal of Parallel and Distributed Computing 16(2): 108-120.10.1016/0743-7315(92)90027-K]Search in Google Scholar
[Sass, R. and Mutka, M. (1994). Enabling unimodular transformations, Proceedings of the 1994 ACM/IEEE Conference on Supercomputing, Washington, DC, USA, pp. 753-762.]Search in Google Scholar
[Strout, M.M., Carter, L., Ferrante, J. and Kreaseck, B. (2004). Sparse tiling for stationary iterative methods, International Journal of High Performance Computing Applications 18(1): 2004.10.1177/1094342004041294]Search in Google Scholar
[Tang, P. and Xue, J. (2000). Generating efficient tiled code for distributed memory machines, Parallel Computing 26(11): 1369-1410.10.1016/S0167-8191(00)00040-5]Search in Google Scholar
[Verdoolaege, S. (2011). Integer set library-manual, http:// www.kotnet.org/~skimo//isl/manual.pdf.]Search in Google Scholar
[Verdoolaege, S. (2012). Barvinok: User guide, Barvinok-0.36, www.garage.kotnet.org/~skimo/barvinok/barvinok.pdf.]Search in Google Scholar
[Verdoolaege, S., Cohen, A. and Beletska, A. (2011). Transitive closures of affine integer tuple relations and their overapproximations, in E. Yahav (Ed.), Proceedings of the 18th international Conference on Static analysis, SAS’11, Springer-Verlag, Berlin/Heidelberg, pp. 216-232.10.1007/978-3-642-23702-7_18]Search in Google Scholar
[Wolf, M.E. and Lam, M.S. (1991). A data locality optimizing algorithm, Proceedings of the ACM SIGPLAN 1991 Conference on Programming Language Design and Implementation, Toronto, Canada, pp. 30-44.]Search in Google Scholar
[Wonnacott, D.G. and Strout, M.M. (2013). On the scalability of loop tiling techniques, Proceedings of the 3rd International Workshop on Polyhedral Compilation Techniques (IMPACT), Berlin, Germany.]Search in Google Scholar
[Wonnacott, D., Jin, T. and Lake, A. (2015). Automatic tiling of mostly-tileable loop nests, IMPACT 2015, 5th International Workshop on Polyhedral Compilation Techniques, Amsterdam, The Netherlands.]Search in Google Scholar
[Xue, J. (1996). Communication-minimal tiling of uniform dependence loops, Languages and Compilers for Parallel Computing, Springer, Berlin/Heidelberg, pp. 330-349.]Search in Google Scholar
[Xue, J. (1997). On tiling as a loop transformation, Parallel Processing Letters 7(4): 409-424.10.1142/S0129626497000401]Search in Google Scholar
[Xue, J. (2012). Loop Tiling for Parallelism, Springer Science & Business Media, Springer-Verlag, New York, NY.]Search in Google Scholar
[Zdunek, R. (2014). Regularized nonnegative matrix factorization: Geometrical interpretation and application to spectral unmixing, International Journal of Applied Mathematics and Computer Science 24(2): 233-247, DOI: 10.2478/amcs-2014-001710.2478/amcs-2014-0017]Search in Google Scholar
