Research On The Iteration Method For One Kind Of The Constraint Solution Of In-line Matrix Equation

The constrained matrix equation problem is to find the solutions of a matrix equation ora system of matrix equations in a constrained matrix set. In recent years, as it has been widelyused in many fields such as linear optimal control problem, the analysis of the main element,structural design, in-linear programming problem, finite element analysis, automatic controltheory, vibration theory and so on, the study of the constrained matrix equation problem hasbecome one important topic in the field of numerical algebra. The in-linear matrix equationproblem has been more widely applied in the fields of scientific computing and engineeringapplication such as biological science, economic theory, engineering technology, appliedphysics, management science and so on. So the study of the in-linear matrix equation problemhas been becoming more important.The master’s graduate thesis mainly study the problem as followGivenA, B,C Rn n,S Rn n. Find X*S, such thatAX*2BX*C0or AX*2BX*C mX inSAX2BX Cwhere S is the set of n order real quadratic matrix, symmetric matrix, anti-symmetricmatrix, central symmetry matrix, central anti-symmetry matrix, bisymmetric matrix,symmetric skew-centro-symmetric matrix.In this thesis, we mainly study using Conjugate gradient method and Newton’s method tofind the constrained solution of the question above. In the end, some numerical examplesare given to verify the efficiency of the algorithms.