Positive Definite Solution Of Nonlinear Matrix Equation

Nonlinear matrix equation has a profound theoretical significance and widespread application background in the field of numerical solution of nonlinear analysis; more and more scholars begin to focus on numerical method for solving the matrix equations. Considering the background of practical significance, study of the positive definite matrix equation solution has important practical significance.Considering above reasons, the paper’s main works are as follows:First chapter for introduction, simple nonlinear matrix equation of this subject at home and abroad, discusses the background significance, development process and development trends, research route and method.The second chapter gives preparatory knowledge, mainly the eigenvalues of the matrix, positive definite matrix, CS of Hermite matrix, matrix decomposition theorem and matrix’s triangular decomposition theorem, the vector norm, matrix norm, the kronecker product of matrix inequalities, references, and functional analysis of compression mapping theorem, Bananch in the field of the fixed point theorem and some other related basic concepts and basic properties.Prove the conclusion to use typical important theorem, etc.The third chapter mainly combined with the recently got definite solutions of matrix equation of scope has carried on the induction, the results are discussed with or the necessary or sufficient conditions for the solution of matrix equation obtained.The fourth chapter is for nonlinear matrix equation of dynamic development at residence and abroad, combining the results of the researchers, on the basis of the conditions of a given matrix a formal, maximum solution of equation converges to the proof, research methods and research route was improved, thus obtained some new results about the matrix equation has a positive definite solution.