In this paper two reasons-the deviation of the data from the origin and the size of the data-causing the ill-conditioned normal equations in the least square fitting of a polynomial are discussed.

It is proved that the polynomial normal operators have the property (p) and the polynomial normal reductive operators must be normal operators.

In this paper, a method for converting GPS height to normal one by means of support vector machine is proposed, and compared with the methods of neural network, polynomial fitting etc.