Про ефективність алгоритмів з багаторівневим паралелізмом: Fìz.-mat. model. ìnf. tehnol. 2021, 33:133-137

• Date: 2021
• Main Authors: Popov, Oleksandr, Chystiakov, Oleksiy
• Format: Article
• Language: Ukrainian
• Published: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Subjects: паралельні алгоритми; коефіцієнти прискорення та ефективності; багаторівнева модель паралельних обчислень; алгебраїчна проблема власних значень
• Online Access: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/216
• Journal Title: Physico-mathematical modeling and informational technologies

The paper investigates the efficiency of algorithms for solving computational mathematics problems that use a multilevel model of parallel computing on heterogeneous computer systems. A methodology for estimating the acceleration of algorithms for computers using a multilevel model of parallel computing is proposed. As an example, the parallel algorithm of the iteration method on a subspace for solving the generalized algebraic problem of eigenvalues of symmetric positive definite matrices of sparse structure is considered. For the presented algorithms, estimates of acceleration coefficients and efficiency were obtained on computers of hybrid architecture using graphics accelerators, on multi-core computers with shared memory and multi-node computers of MIMD-architecture. References Popov, А. V., Rudich, O. V., Chistyakov, А. V. (2018). Multi-level Model of Parallel Computing for Linear Algebra Problems. Problems of Programming, 2–3, 83–92. Khimich, A. N., Molchanov, I. N., Popov, A. V., Chistyakova, T. V., Yakovlev, M. F. (2008). Parallel Algorithms for the Solving of Computational Mathematics Problems. [in Russian], Naukova Dumka, Kyiv. Khimich, A. N., Dekret, V. А., Popov, A. V., Chistyakov, A. V. (2018). Numerical Study of the Stability of Composite Materials on Computers of Hybrid Architecture [in Russian]. Journal of Automation and Information Sciences, 2018, 4, 1–17. DOI https://doi.org/10.1615/jautomatinfscien.v50.i7.20 Khimich, A. N., Popov, A. V., Chistyakov, A. V. (2017). Hybrid Algorithms for Solving the Algebraic Eigenvalue Problem with Sparse Matrices. [in Russian]. Cybernetics and Systems Analysis, 6, 132-146. DOI https://doi.org/10.1007/s10559-017-9996-5 Popov, O. V., Rudich, O. V. (2017). On the Solving of Linear Systems on Hybrid-Architecture Computers [in Ukrainian]. Mathematical and computer modeling. Series: Physics and Mathematics: Sb. sciences works, 15, 158-164.