Research On Iterative Algorithm Of Constrained Matrix Equation AXB=C

Constraint matrix equation problem refers to solving the solution of matrix equation in a given set of constraints.Different constraints and different linear matrix equations can be obtained in different application backgrounds.Constraint matrix equations are widely used in many fields,such as cybernetics,information theory,parameter identification,financial theory,electricity,biology,vibration theory,time series analysis,structural design,etc.Therefore,it is of certain value and significance to study matrix equations.This dissertation mainly gives the solutions and numerical comparisons of different algorithms for the same problem.The thesis mainly studies the following problems:Problem Ⅰ.Given matrix A ∈ Rmxn,B ∈ Rn×p,C ∈ Rmxp,X ∈ Rn×n.Find X ∈ Ω,such that Where Ω={X|AXB=C,XT=X｝.Problem Ⅱ Given matrix A ∈ Rm×n,B ∈ Rn×p C ∈ Rm×p.Find X ∈ Ω,such thatWhere Ω=｛X |‖AXB-C‖F2=min,X=XT｝.Problem Ⅲ Given matrix A ∈ Rm×n,B ∈ Rn×p,C ∈ Rm×p.Find X,such that Where Ω={x | X=XT,X≥0}.Firstly,the best approximate symmetric solution and the least square best approximate symmetric solution of the matrix equation AXB=C are discussed,the solutions and numerical comparisons of DRS algorithm,Dykstra algorithm and LSQR algorithm are given,and the specific calculation method of each subproblem under each algorithm is discussed.Secondly,the least square nonnegative symmetric solution of the matrix equation AXB=C is discussed.The solutions and numerical comparisons of ADMM algorithm,SPG algorithm and DRS algorithm are given.Finally,the fixed point iterative algorithm for solving the least square non-negative symmetric solution of matrix equation AXB=C and its Anderson accelerated solution and numerical comparison are given.