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The slope calculation algorithm is one of the most widely used geospatial algorithms employing the 3x3 moving window technique (along with calculation of aspect, curvature and flow direction). This work presents an approach consisting of transforming a slope algorithm from a sequential form into a version that can exploit vector and parallel traits of multicore architectures with vector instructions. This approach allows us to take advantage of the potential of the modern multicore processors. The basic idea for optimizing the 3x3 moving window computation is to split the equation used to calculate the result into parts that operate on data that are known to exist in adjacent memory locations. The research was conducted on two multicore architectures without the change in the code — the older architecture was Sandy Bridge and the newer one was Haswell (with more cores). The efficiency of the developed slope algorithm was verified in practice with the use of DEM files of the same resolution but of different sizes. We showed through the numerical experiments that our approach gives better time performance than the original algorithm (and other tools) — and with no loss of accuracy. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate dense linear algebra algorithms on shared memory multicore architectures. The design and implementation of a parallel tiled WZ factorization algorithm which can fully exploit such architectures are presented. Three parallel implementations of the algorithm are studied. The first one relies only on exploiting multithreaded BLAS (basic linear algebra subprograms) operations. The second implementation, except for BLAS operations, employs the OpenMP standard to use the loop-level parallelism. The third implementation, except for BLAS operations, employs the OpenMP task directive with the depend clause. We report the computational performance and the speedup of the parallel tiled WZ factorization algorithm on shared memory multicore architectures for dense square diagonally dominant matrices. Then we compare our parallel implementations with the respective LU factorization from a vendor implemented LAPACK library. We also analyze the numerical accuracy. Two of our implementations can be achieved with near maximal theoretical speedup implied by Amdahl’s law. [ABSTRACT FROM AUTHOR]