CASPIAN JOURNAL
MANAGEMENT AND HIGH TECHNOLOGIES
VECTORIZATION OF ALGORITHMS FOR SOLVING OF EIGENVALUES AND SINGULAR VALUE PROLEMS USING THE HOUSEHOLDER TRANSFORMATIONS
 |
Read | Egunov Vitaly A., Andreev Andrey E. VECTORIZATION OF ALGORITHMS FOR SOLVING OF EIGENVALUES AND SINGULAR VALUE PROLEMS USING THE HOUSEHOLDER TRANSFORMATIONS // Caspian journal : management and high technologies. — 2020. — №2. — pp. 71-85. |
Egunov Vitaly A. - Volgograd State Technical University, vegunov@mail.ru
Andreev Andrey E. - Volgograd State Technical University, andan2005@yandex.ru
The vectorization of algorithms for proper and singular expansions of General - type matrices, and use the householder reflection transform as the base transformation are considered. Vectorization of calculations, which is a type of parallelization, is an effective tool for improving the performance of programs, in which single - threaded applications can perform several similar operations simultaneously. Modern compilers can perform automatic vectorization of calculations, i.e. convert programs from a scalar representation to a vector implementation. The article analyzes the effectiveness of automatic vectorization performed by modern compilers, and considers the problems inherent in automatic vectorization. The author's algorithm for vectorization of calculations for algorithms of proper and singular expansions of General square matrices is proposed. The proposed solutions allow significantly increasing the speed of software implementation of these transformations. The paper presents the features of the vectorization process and the results of computational experiments.
Key words: квадратные матрицы, собственное разложение, сингулярное разложение, преобразование отражения, преобразование Хаусхолдера, эффективность программ, ускорение работы программ, векторизация вычислений, автоматическая векторизация, оптимизирующие компиляторы,