It is given that twonew solving methods,the first method proves that an algebraic function is a solution withthe help of analytic exfension and using the value of many--valued analytic function is different on the two sides of the fracture, then second method is obtained.

Least square fitting of pump characteristic curve by orthogonal function;

This paper introduced the basic principle to acquire height anomaly using orthogonal function,took the control surveying results of Hufengling section of Suiman road in Heilongjiang to testify,and drew specific conclusions which is valuable to direct engineering height surveying.

Using the orthogonal function system mixed a weight function as the basis function,the drawback of forming an ill-conditioned system of equations for the moving least-square approximation method is overcome.

To apply finite element method in signal processing, the elements were orthogonalized based on group theory to form a series of orthogonal functions in a cyclic zone,and the orthogonal functions were applied in function approximation.

It introduces a method based on orthogonal functions for elevation abnormal fitting used in linear area.