Regularization to orthogonal-polynomials fitting with application to magnetization data

An obstacle encountered in applying orthogonal-polynomials fitting is how to select out the proper fitting expression. By adding a Laplace term to the error expression and introducing the concept of overfitting degree, a regularization and corresponding cross validation scheme is proposed for two-variable polynomials fitting. While the Fortran implementation of above scheme is applied to magnetization data, a satisfactory fitting precision is reached, and overfitting problem can be quantitatively assessed, which therefore offers the quite reliable base for future comprehensive investigations of magnetocaloric and phase-transition properties of magnetic functional materials.