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 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 LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS IN ARROWHEAD FORM

2021 ◽  
pp. 557
Author(s):  
Ivana Jovović
Keyword(s):  
Differential Equations ◽  
Linear Systems ◽  
Characteristic Matrix ◽  
System Matrix ◽  
First Order ◽  
Systems Of Differential Equations ◽  
Algebraic Properties ◽  
Arrowhead Matrix ◽  
Invariant Factors ◽  
First Order Differential Equations

This paper deals with different approaches for solving linear systems of the first order differential equations with the system matrix in the symmetric arrowhead form.Some needed algebraic properties of the symmetric arrowhead matrix are proposed.We investigate the form of invariant factors of the arrowhead matrix.Also the entries of the adjugate matrix of the characteristic matrix of the arrowhead matrix are considered. Some reductions techniques for linear systems of differential equations with the system matrix in the arrowhead form are presented.

The Linear System Solver of Programs Named CORTH and KYLIN2

2017 ◽  
Author(s):  
Pingzhou Ming ◽  
Junjie Pan ◽  
Xiaolan Tu ◽  
Dong Liu ◽  
Hongxing Yu
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Nuclear Power ◽  
Experimental Results ◽  
Gmres Method ◽  
Thermal Hydraulics ◽  
Lattice Calculation ◽  
Minimal Residual

Sub-channel thermal-hydraulics program named CORTH and assembly lattice calculation program named KYLIN2 have been developed in Nuclear Power Institute of China (NPIC). For the sake of promoting the computing efficiency of these programs and achieving the better description on fined parameters of reactor, the programs’ structure and details are interpreted. Then the characteristics of linear systems of these programs are analyzed. Based on the Generalized Minimal Residual (GMRES) method, different parallel schemes and implementations are considered. The experimental results show that calculation efficiencies of them are improved greatly compared with the serial situation.

scholarly journals Formulae of partial reduction for linear systems of first order operator equations

2010 ◽  
Vol 23 (11) ◽  
pp. 1367-1371 ◽  
Author(s):  
Branko Malešević ◽  
Dragana Todorić ◽  
Ivana Jovović ◽  
Sonja Telebaković
Keyword(s):  
Linear Systems ◽  
Partial Reduction ◽  
Order Operator ◽  
Operator Equations ◽  
First Order

scholarly journals (M,β)-Stability of Positive Linear Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Octavian Pastravanu ◽  
Mihaela-Hanako Matcovschi
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Transient Behavior ◽  
Short Term ◽  
Time Dynamics ◽  
The Right ◽  
Long Term Behavior ◽  
Stability Concept

The main purpose of this work is to show that the Perron-Frobenius eigenstructure of a positive linear system is involved not only in the characterization of long-term behavior (for which well-known results are available) but also in the characterization of short-term or transient behavior. We address the analysis of the short-term behavior by the help of the “(M,β)-stability” concept introduced in literature for general classes of dynamics. Our paper exploits this concept relative to Hölder vectorp-norms,1≤p≤∞, adequately weighted by scaling operators, focusing on positive linear systems. Given an asymptotically stable positive linear system, for each1≤p≤∞, we prove the existence of a scaling operator (built from the right and left Perron-Frobenius eigenvectors, with concrete expressions depending onp) that ensures the best possible values for the parametersMandβ, corresponding to an “ideal” short-term (transient) behavior. We provide results that cover both discrete- and continuous-time dynamics. Our analysis also captures the differences between the cases where the system dynamics is defined by matrices irreducible and reducible, respectively. The theoretical developments are applied to the practical study of the short-term behavior for two positive linear systems already discussed in literature by other authors.

scholarly journals A Modification of Minimal Residual Iterative Method to Solve Linear Systems

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Xingping Sheng ◽  
Youfeng Su ◽  
Guoliang Chen
Keyword(s):  
Linear System ◽  
Iterative Method ◽  
Linear Systems ◽  
Residual Error ◽  
Projection Technique ◽  
Numerical Example ◽  
Minimal Residual

We give a modification of minimal residual iteration (MR), which is 1V-DSMR to solve the linear systemAx=b. By analyzing, we find the modifiable iteration to be a projection technique; moreover, the modification of which gives a better (at least the same) reduction of the residual error than MR. In the end, a numerical example is given to demonstrate the reduction of the residual error between the 1V-DSMR and MR.

scholarly journals A saddle point type solution for a system of operator equations

2021 ◽  
pp. 1-12
Author(s):  
Piotr Kowalski
Keyword(s):  
Saddle Point ◽  
Minimax Theorem ◽  
Dirichlet Problems ◽  
Type Solution ◽  
Operator Equations ◽  
Potential Operators ◽  
System Of Operator Equations ◽  
Ky Fan ◽  
Point Type

Let Ω⊂Rn n>1 and let p,q≥2. We consider the system of nonlinear Dirichlet problems equation* brace(Au)(x)=Nu′(x,u(x),v(x)),x∈Ω,r-(Bv)(x)=Nv′(x,u(x),v(x)),x∈Ω,ru(x)=0,x∈∂Ω,rv(x)=0,x∈∂Ω,endequation* where N:R×R→R is C1 and is partially convex-concave and A:W01,p(Ω)→(W01,p(Ω))* B:W01,p(Ω)→(W01,p(Ω))* are monotone and potential operators. The solvability of this system is reached via the Ky–Fan minimax theorem.

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