Construction Method of Regularization by Singular Value Decomposition of Design Matrix

Tikhonov regularization introduces regularization parameter and stable functional to improve the ill-condition. When the stable functional expressed as two-norm constraint, the regularization method is the same as ridge estimation. The analysis of the variance and bias of the ridge estimation shows that ridge estimation improved the ill-condition but introduced more bias. The estimation reliability is lowered. We get that correct the larger singular values cannot decrease the variance effectively but introduced more bias, correcting the smaller singular values can decrease the variance effectively. We choose the eigenvectors of the smaller singular values to construct the regularization matrix. It can adjust the correction of the singular values, decrease the variance and biases and finally get a more reliable estimation