scholarly journals A note on the reduction formulas for some systems of linear operator equations

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1353-1362
Author(s):  
Ivana Jovovic ◽  
Branko Malesevic
Keyword(s):  
Linear System ◽  
Linear Operator ◽  
The Other ◽  
Characteristic Matrix ◽  
System Matrix ◽  
Operator Equations ◽  
Rational Form ◽  
Total Reduction ◽  
Linear Operator Equations

We consider partial and total reduction of a nonhomogeneous linear system of the operator equations with the system matrix in the same particular form as in paper [7]. Here we present two different concepts. One is concerned with partially reduced systems obtained by using the Jordan and the rational form of the system matrix. The other one is dealing with totally reduced systems obtained by finding the adjugate matrix of the characteristic matrix of the system matrix.

scholarly journals Total reduction of linear systems of operator equations with the system matrix in the companion form

2013 ◽  
Vol 93 (107) ◽  
pp. 117-126
Author(s):  
Ivana Jovovic
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Characteristic Matrix ◽  
System Matrix ◽  
Operator Equations ◽  
Total Reduction ◽  
System Of Operator Equations ◽  
Separated Variables

We consider a total reduction of a nonhomogeneous linear system of operator equations with the system matrix in the companion form. Totally reduced system obtained in this manner is completely decoupled, i.e., it is a system with separated variables. We introduce a method for the total reduction, not by a change of basis, but by finding the adjugate matrix of the characteristic matrix of the system matrix. We also indicate how this technique may be used to connect differential transcendence of the solution with the coefficients of the system.

scholarly journals Differential transcendence of solutions of systems of linear differential equations based on total reduction of the system

2020 ◽  
pp. 24-24
Author(s):  
Ivana Jovovic
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Complex Field ◽  
System Matrix ◽  
Operator Equations ◽  
Total Reduction ◽  
Commuting Operators ◽  
Constant Coefficients ◽  
Linear Differential ◽  
System Of Operator Equations

In this paper we consider total reduction of the nonhomogeneous linear system of operator equations with constant coefficients and commuting operators. The totally reduced system obtained in this manner is completely decoupled. All equations of the system differ only in the variables and in the nonhomogeneous terms. The homogeneous parts are obtained using the generalized characteristic polynomial of the system matrix. We also indicate how this technique may be used to examine differential transcendence of the solution of the linear system of the differential equations with constant coefficients over the complex field and meromorphic free terms.

scholarly journals Minimization of Tikhonov Functionals in Banach Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-19 ◽  
Author(s):  
Thomas Bonesky ◽  
Kamil S. Kazimierski ◽  
Peter Maass ◽  
Frank Schöpfer ◽  
Thomas Schuster
Keyword(s):  
Linear Operator ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Dual Space ◽  
Descent Method ◽  
The Other ◽  
Steepest Descent Method ◽  
Operator Equations ◽  
Underlying Space ◽  
Linear Operator Equations

Tikhonov functionals are known to be well suited for obtaining regularized solutions of linear operator equations. We analyze two iterative methods for finding the minimizer of norm-based Tikhonov functionals in Banach spaces. One is the steepest descent method, whereby the iterations are directly carried out in the underlying space, and the other one performs iterations in the dual space. We prove strong convergence of both methods.

On nonnegative solvability of linear operator equations

1994 ◽  
Vol 18 (1) ◽  
pp. 88-108 ◽  
Author(s):  
Ruey-Jen Jang-Lewis ◽  
Harold Dean Victory
Keyword(s):  
Linear Operator ◽  
Operator Equations ◽  
Linear Operator Equations
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