SPECTRAL DECOMPOSITRION FORMULA FOR REGULARIZATION SOLUTION OF ILL-POSED EQUATION

摘要

This paper discusses the regularization solution of ill-posed equation with the help of its spectral decomposition formula. It shows that regularization can filter the influence of the high frequency errors which are very sensitive to the parameters to be estimated, and gives a complete derivation of the spectral decomposition formulae of least squares adjustment, rank-deficient adjustment and the regularization solution of ill-posed equation. It also shows the equivalence between the trace of the mean squares error and the expectation of the second norm of estimated parameter's total error.