Application of Iterative Calculation of Matrix for Solving Ill-posed Problems

The parameter estimations are unstable when the determinant of the coefficient matrix of the normal equation is closed to 0 in least-squares estimation. The deviation of estimator is too great because of rounding error of calculator and it is hard to get the precise inverse of the coefficient matrix. A matrix function which is matrix power series was introduced in proposed method based on ridge estimation. The matrix function is convergent to the normal equation coefficient matrix inverse and can be calculated through iterative calculation of matrix. Then the accuracy of the matrix inverse is improved and the estimations are robust. Three methods which are least-squares estimation, ridge estimation and iterative calculation were investigated. The second one is a biased estimation and it is difficult to get the appropriate ridge parameter, the third one is infinite times of calculation. The Theoretical analysis and computer simulation results show that the iterative calculation is precise and effective.