CASPIAN JOURNAL
MANAGEMENT AND HIGH TECHNOLOGIES
CACHE-OPTIMIZATION OF SOLVING EIGENVALUES PROBLEM FOR PARALLEL COMPUTING SYSTEMS
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Read | Egunov Vitaly A. CACHE-OPTIMIZATION OF SOLVING EIGENVALUES PROBLEM FOR PARALLEL COMPUTING SYSTEMS // Caspian journal : management and high technologies. — 2019. — №1. — pp. 154-163. |
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Egunov Vitaly A. - Cand. Sci. (Engineering), Volgograd State Technical University, 28 Lenin Ave., Volgograd, 400005, Russian Federation, vegunov@mail.ru
The reduction of the matrix to Hessenberg form in the framework of the problem of calculating eigenvalues on parallel computing systems with shared memory is considered. Parallel computing systems with shared memory are the most common and affordable type of parallel computing systems. As the base conversion use the conversion reflections of Householder. The article analyzes the solution of the problem of reducing the matrix to Hessenberg form on the target computing architectures, with special attention paid to the optimization of algorithms in terms of efficient use of cache memory. The author's algorithms for solving the problem, which are optimized versions of the classical householder transformation, are presented. The use of these algorithms can significantly reduce the execution time of the program. The conclusions are confirmed by the results of computational experiments.
Key words: собственные числа, собственные значения, собственное разложение, преобразование отражения, преобразование Хаусхолдера, многоядерные процессоры, многопроцессорные системы, неоднородные параллельные вычислительные системы, эффективность программ, ускорение