scholarly journals A Peek into Theory of Automation with Applications to Various Branches of Science

2020 ◽  
Vol 9 (09) ◽  
pp. 25156-25160
Author(s):  
Divyalaxmi N.
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Least Square ◽  
Uniqueness Of Solution ◽  
Characteristic Matrix ◽  
Point Boundary ◽  
Difference System ◽  
Lattice Vector ◽  
First Order

In this paper, we shall be concerned with the existence and uniqueness of solution to three- point boundary value problems associated with a system of first order matrix difference system. Shortest and Closest Lattice vector methods are used as a tool to obtain the best least square solution of the  three-point boundary value problems when  the characteristic matrix D is rectangular. In this paper, we shall be concerned with the existence and uniqueness of solution to three- point boundary value problems associated with a system of first order matrix difference system. Shortest and Closest Lattice vector methods are used as a tool to obtain the best least square solution of the  three-point boundary value problems when  the characteristic matrix D is rectangular. 

scholarly journals Kronecker Product of matrices and their applications to self-adjoint two-point boundary value problems associated with first order matrix differential systems

2021 ◽  
Vol 10 (10) ◽  
pp. 25399-25407
Author(s):  
Sriram Bhagavatula ◽  
Dileep Durani Musa ◽  
Murty Kanuri
Keyword(s):  
Boundary Value Problems ◽  
Kronecker Product ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Least Square ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Differential Systems ◽  
First Order ◽  
Product Of Matrices

In this paper, we shall be concerned with Kronecker product or Tensor product of matrices and develop their properties in a systematic way. The properties of the Kronecker product of matrices is used as a tool to establish existence and uniqueness of solutions to two-point boundary value problems associated with system of first order differential systems. A new approach is described to solve the Kronecker product linear systems and establish best least square solutions to the problem. Several interesting examples are given to highlight the importance of Kronecker product of matrices. We present adjoint boundary value problems and deduce a set of necessary and sufficient conditions for the Kronecker product boundary value problem to be self-adjoint.

scholarly journals Generalized two point boundary value problems. existence and uniqueness

1992 ◽  
Vol 5 (2) ◽  
pp. 147-156
Author(s):  
K. N. Murty ◽  
S. Sivasundaram
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Matrix Differential Equations ◽  
Matrix Differential ◽  
Pseudo Inverse

An algorithm is presented for finding the pseudo-inverse of a rectangular matrix. Using this algorithm as a tool, existence and uniqueness of solutions to two point boundary value problems associated with general first order matrix differential equations are established.

Two-Point Boundary Value Problems for First Order Causal Difference Equations

2020 ◽  
Vol 51 (4) ◽  
pp. 1399-1416
Author(s):  
Wen-Li Wang ◽  
Jing-Feng Tian ◽  
Wing-Sum Cheung
Keyword(s):  
Boundary Value Problems ◽  
Difference Equations ◽  
Boundary Value ◽  
Point Boundary ◽  
First Order
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