Applications of Vector Matrix Operations

State contains the results of a study of the specifics, possibilities and advantages of fast algorithms. This paper focuses on the description of the proposed approach for the development of fast algorithms using vector-matrix operations.

Download Full-text

Fuzzy cognitive modeling of heterogeneous electromechanical systems

Journal Of Applied Informatics ◽

10.37791/2687-0649-2021-16-1-32-39 ◽

2021 ◽

Vol 16 (91) ◽

pp. 32-39

Author(s):

Vadim V. Borisov ◽

◽

Sergey P. Kurilin ◽

Nikolai N. Prokimnov ◽

Margarita V. Chernovalova ◽

...

Keyword(s):

Vector Space ◽

Cognitive Modeling ◽

Angular Position ◽

Technical Condition ◽

Cognitive Models ◽

Innovative Design ◽

Electromechanical Systems ◽

Problem Situations ◽

Matrix Operations ◽

Vector Matrix

The article presents a method of fuzzy cognitive modeling for heterogeneous electromechanical systems (HEMSs) in the management of innovative design solutions. During the operation of the HEMSs, as a result of their operational aging, the properties of the windings parametric matrices and the HEMSs vector space properties change. Periodic testing of the HEMSs vector space allows obtaining reliable information about the current technical condition of the HEMSs, about its changes during operation and about the risks of operating capability loss. At the same time (I) the presence of proportional changes in signals during sequential testing indicates the homogeneous operational aging of the HEMSs and its rate; (II) a disproportionate change in one of the signals indicates the damage or the development of a heterogeneous aging process; (III) a change in signals with a change in the angular position of the rotor indicates worn bearings or damage of the HEMSs rotor. The article presents the HEMSs model, describes the method for the topological research of the vector space and the method for forming the diagnostic matrices. The deviations of their elements are fuzzy due to the uncertainty of the load, influencing environmental factors and unstable supply voltages. Therefore, for predictive estimation of the HEMSs state, it is proposed to use fuzzy relational cognitive models that allow implementing a completely fuzzy approach to modeling problem situations in these systems. The presented data confirm the growth of the HEMSs heterogeneity under conditions of uncertainty of external influences. The proposed method for predictive estimation of the HEMSs state, based on fuzzy relational cognitive models, provides resistance to an increase in the uncertainty of the estimation results for various models of system dynamics due to a reasonable set of fuzzy vector-matrix operations.

Download Full-text

A MODEL FOR EVENTS MONITORING HETEROGENEOUS DISTRIBUTED DATABASES BASED ON VECTOR-MATRIX OPERATIONS

Far East Journal of Electronics and Communications ◽

10.17654/ec016030645 ◽

2016 ◽

Vol 16 (3) ◽

pp. 645-656

Author(s):

Vadym Mukhin ◽

Yaroslav Kornaga ◽

Yevhenii Mostovyi ◽

Yurii Bazaka

Keyword(s):

Distributed Databases ◽

Matrix Operations ◽

Vector Matrix

Download Full-text

Possible improvement of computer performance by increasing the speed of vector-matrix operations

Cybernetics ◽

10.1007/bf01072306 ◽

1979 ◽

Vol 15 (1) ◽

pp. 142-147

Author(s):

V. A. Vyshinskii ◽

Z. L. Rabinovich

Keyword(s):

Computer Performance ◽

Matrix Operations ◽

Vector Matrix

Download Full-text

Appendix A: Summary of Vector/Matrix Operations

Advanced Kalman Filtering, Least-Squares and Modeling ◽

10.1002/9780470890042.app1 ◽

2011 ◽

pp. 555-568

Keyword(s):

Matrix Operations ◽

Vector Matrix

Download Full-text

Simultaneous Multithreaded Matrix Processor

Journal of Circuits System and Computers ◽

10.1142/s0218126615501145 ◽

2015 ◽

Vol 24 (08) ◽

pp. 1550114

Author(s):

Mostafa I. Soliman ◽

Elsayed A. Elsayed

Keyword(s):

Parallel Execution ◽

Parallel Applications ◽

Instruction Level Parallelism ◽

Hardware Complexity ◽

Data Parallel ◽

Matrix Vector Multiplication ◽

Givens Rotation ◽

Matrix Operations ◽

Vector Matrix ◽

Level Parallelism

This paper proposes a simultaneous multithreaded matrix processor (SMMP) to improve the performance of data-parallel applications by exploiting instruction-level parallelism (ILP) data-level parallelism (DLP) and thread-level parallelism (TLP). In SMMP, the well-known five-stage pipeline (baseline scalar processor) is extended to execute multi-scalar/vector/matrix instructions on unified parallel execution datapaths. SMMP can issue four scalar instructions from two threads each cycle or four vector/matrix operations from one thread, where the execution of vector/matrix instructions in threads is done in round-robin fashion. Moreover, this paper presents the implementation of our proposed SMMP using VHDL targeting FPGA Virtex-6. In addition, the performance of SMMP is evaluated on some kernels from the basic linear algebra subprograms (BLAS). Our results show that, the hardware complexity of SMMP is 5.68 times higher than the baseline scalar processor. However, speedups of 4.9, 6.09, 6.98, 8.2, 8.25, 8.72, 9.36, 11.84 and 21.57 are achieved on BLAS kernels of applying Givens rotation, scalar times vector plus another, vector addition, vector scaling, setting up Givens rotation, dot-product, matrix–vector multiplication, Euclidean length, and matrix–matrix multiplications, respectively. The average speedup over the baseline is 9.55 and the average speedup over complexity is 1.68. Comparing with Xilinx MicroBlaze, the complexity of SMMP is 6.36 times higher, however, its speedup ranges from 6.87 to 12.07 on vector/matrix kernels, which is 9.46 in average.

Download Full-text