The Iterative Algorithm Of A Type Of Linear Matrix Equations For The Reflexive Solution

Linear matrix equations have been widely applied in control theory,neuralnetwork design, structure design and application, linear optimal control,etc. Thesolving the linear matrix equations has attracted the attention of scholars homeand abroad, and fruitful results have been achieved.By constructing a new iterative algorithm based on the conjugate gradient,the paper studies the solution of linear matrix equation,respectively. Meanwhile,we proved the convergence of the algorithm by using the matrix norm and theproperty of trace. Then, the efectiveness of this algorithm will be tested by nu-merical examples. The main contents are described as follows.In chapter one, we frst introduced some background knowledge for linearmatrix equation problem. And then, we introduced some basic symbols and def-initions used in our paper.In chapter two, the antisymmetric solution of matrix equations problemsA1XB1+C1XD1=F1, A2XB2+C2XD2=F2is studied. We constructeda new iterative algorithm, gave the antisymmetric solutions when equations areconsistent and the optimum approximate solution by using the conjugate gra-dient method. The efectiveness of this algorithm will be tested by numericalexamples.In chapter three, the reflexive solutions of the matrix equations AXB+CXD=F and A1XB1+C1XD1=F1, A2XB2+C2XD2=F2is studied, re-spectively.Based on the conjugate gradient method, we design a more efectivealgorithm, and provide both the the reflexive solutions&the least squares reflex-ive solution. Finally, the efectiveness of this algorithm will be tested by numericalexamples.