Revisiting the Adjoint Matrix for FPGA Calculating the Triangular Matrix Inversion

Author(s):  
Di Yan ◽  
Wei-Xing Wang ◽  
Lei Zuo ◽  
Xiao-Wei Zhang
1990 ◽  
Vol 14 (2) ◽  
pp. 223-228 ◽  
Author(s):  
Basile Louka ◽  
Maurice Tchuente

Author(s):  
Rusul Khalil Saad ◽  
Safaa S. Omran

Many systems like the control systems and in communication systems, there is usually a demand for matrix inversion solution. This solution requires many operations, which makes it not possible or very hard to meet the needs for real-time constraints. Methods were exists to solve this kind of problems, one of these methods by using the LU decomposition of matrix which is a good alternative to matrix inversion. The LU matrices are two matrices, the L matrix, which is a lower triangular matrix, and the U matrix, which is an upper triangular matrix. In this paper, a design of dual-core processor is used as the hardware of the work and certain software was written to enable the two cores of the dual-core processor to work simultaneously in computing the value of the L matrix and U matrix. The result of this work are compared with other works that using single-core processor, and the results found that the time required in the cores of the dual-core is more less than using single-core. The designed dual-core processor is invoked using the VHDL language.


2020 ◽  
Vol 18 (1) ◽  
pp. 353-377 ◽  
Author(s):  
Zhien Li ◽  
Chao Wang

Abstract In this study, we obtain the scalar and matrix exponential functions through a series of quaternion-valued functions on time scales. A sufficient and necessary condition is established to guarantee that the induced matrix is real-valued for the complex adjoint matrix of a quaternion matrix. Moreover, the Cauchy matrices and Liouville formulas for the quaternion homogeneous and nonhomogeneous impulsive dynamic equations are given and proved. Based on it, the existence, uniqueness, and expressions of their solutions are also obtained, including their scalar and matrix forms. Since the quaternion algebra is noncommutative, many concepts and properties of the non-quaternion impulsive dynamic equations are ineffective, we provide several examples and counterexamples on various time scales to illustrate the effectiveness of our results.


Sign in / Sign up

Export Citation Format

Share Document