scholarly journals On the Kronecker Product of Matrices and Their Applications To Linear Systems Via Modified QR-Algorithm

2021 ◽  
Vol 10 (6) ◽  
pp. 25352-25359
Author(s):  
Vellanki Lakshmi N. ◽  
Jajula Madhu ◽  
Musa Dileep Durani
Keyword(s):  
Kronecker Product ◽  
Polynomial Matrix ◽  
Singular Value ◽  
Least Square ◽  
Kronecker Products ◽  
Product System ◽  
Qr Algorithm ◽  
Value Decomposition ◽  
The Relationship ◽  
Product Of Matrices

This paper studies and supplements the proofs of the properties of the Kronecker Product of two matrices of different orders. We observe the relation between the singular value decomposition of the matrices and their Kronecker product and the relationship between the determinant, the trace, the rank and the polynomial matrix of the Kronecker products.  We also establish the best least square solutions of the Kronecker product system of equations by using modified QR-algorithm.

Three Point Boundary Value Problems Associated with First Order Fuzzy Difference Systems-Existence and Uniqueness via the Best Least Square Solution

2021 ◽  
Vol 10 (1) ◽  
pp. 25275-25283
Author(s):  
Swapna N ◽  
Udaya Kumar Susarla
Keyword(s):  
Existence And Uniqueness ◽  
Singular Value ◽  
Least Square ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Qr Algorithm ◽  
Difference Systems ◽  
Value Decomposition ◽  
Fuzzy Linear Systems

This paper presents a criteria for the existence and uniqueness of solutions to first order fuzzy difference system using QR-algorithm. Modified QR-algorithm is presented for fuzzy linear systems using singular value decomposition.

System Identification of a Rotor System With Hydrodynamic Bearing by Eigensystem Realization Algorithm (ERA) With an Optimum Doping Signal

2006 ◽  
Author(s):  
T. N. Shiau ◽  
C. H. Cheng ◽  
M. S. Tsai
Keyword(s):  
System Identification ◽  
Singular Value ◽  
Eigensystem Realization Algorithm ◽  
Accurate Identification ◽  
Theoretical Derivation ◽  
Noise Effect ◽  
Hydrodynamic Bearing ◽  
Signal Simulation ◽  
Value Decomposition ◽  
The Relationship

This paper proposes a system identification methodology by using eigensystem realization algorithm (ERA) with doping an optimum signal such that the noise effect can be attenuated and more accurate identification results of y-direction dynamics of a hydrodynamic bearing can be obtained. The technique of optimum doping signal integrates the optimization process with singular value decomposition (SVD) technique to achieve nice removal of the noise. Theoretical derivation is given to interpret the function of the optimum signal and explain the relationship between SVD and optimum signal. Simulation result shows that this proposed ERA with a novel optimum signal is more accurate as compared to the case without optimum signal.

Solving the Robot-World/Hand-Eye Calibration Problem Using the Kronecker Product

2013 ◽  
Vol 5 (3) ◽  
Author(s):  
Mili Shah
Keyword(s):  
Kronecker Product ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Accurate Method ◽  
Form Solution ◽  
Singular Value ◽  
Error Metrics ◽  
Calibration Problem ◽  
Value Decomposition

This paper constructs a separable closed-form solution to the robot-world/hand-eye calibration problem AX = YB. Qualifications and properties that determine the uniqueness of X and Y as well as error metrics that measure the accuracy of a given X and Y are given. The formulation of the solution involves the Kronecker product and the singular value decomposition. The method is compared with existing solutions on simulated data and real data. It is shown that the Kronecker method that is presented in this paper is a reliable and accurate method for solving the robot-world/hand-eye calibration problem.

scholarly journals Multidimensional Arrays, Indices and Kronecker Products

Econometrics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 18
Author(s):  
D. Stephen G. Pollock
Keyword(s):  
Matrix Algebra ◽  
Kronecker Product ◽  
Kronecker Products ◽  
Multidimensional Arrays ◽  
Conventional Notation ◽  
Index Notation ◽  
Product Of Matrices

Much of the algebra that is associated with the Kronecker product of matrices has been rendered in the conventional notation of matrix algebra, which conceals the essential structures of the objects of the analysis. This makes it difficult to establish even the most salient of the results. The problems can be greatly alleviated by adopting an orderly index notation that reveals these structures. This claim is demonstrated by considering a problem that several authors have already addressed without producing a widely accepted solution.

scholarly journals SMART POVERTY ALLEVIATION ARCHITECTURE BASED ON GEOMATICS BIG DATA

2020 ◽  
Vol XLII-3/W10 ◽  
pp. 45-48
Author(s):  
S. Wu ◽  
R. C. Qu ◽  
C. L. Pan ◽  
Z. Y. Bao ◽  
X. J. Feng
Keyword(s):  
Big Data ◽  
Correlation Analysis ◽  
Poverty Alleviation ◽  
Rapid Development ◽  
Singular Value ◽  
Digital City ◽  
Recommendation Algorithm ◽  
Access Methods ◽  
Value Decomposition ◽  
The Relationship

Abstract. With the rapid development of geomatics industry, it has accumulated a large amount of data such as digital city and national geoinformation survey, entered the geomatics big data era. At present, there are some researches on the collection and display of poverty alleviation based on geomatics. However, there are relatively few studies on smart poverty alleviation. Many problems need to be solved. It proposes a smart poverty alleviation architecture based on large geomatics data.It realizes the collection and monitor of smart poverty alleviation in administrative regions at all Levels, such as household, village, Township and county.It realizes the visualization of smart poverty alleviation with geomatics big data.It can poverty alleviation recommendation precisely.Aiming at this model,it proposes a precise poverty alleviation recommendation algorithm based on multi-dimensional correlation analysis. It uses Higher Order Singular Value Decomposition (HOSVD) algorithm to mine the relationship between geomatics and poverty alleviation, and recommends poverty alleviation policies. The research has certain practice and test. The architecture can effectively recommend poverty alleviation assistance policies, improve the efficiency of poverty alleviation archives collation, shorten the period of poverty alleviation archives collation, and improve the storage and access methods of poverty alleviation archives. It improves the efficiency of poverty alleviation collection, monitoring and assistance.

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