Several algorithms for wavefront fitting using Zernike polynomial are studied. In order to avoid the computational error introduced by direct constructing normal equation group

the algorithms can be divided into two classes. One is Gram-Schmidt or covariance matrix method

in which we transform the base function set to meliorate the condition of the normal equation group. The other is called Householder transformation method

in which the matrix of inconsistent equation group is orthogonalized and triangulated using Householder transformation

and then the Zernike coefficients can be worked out by using a backsubstitution technique. It is proposed for the first time. Being a method that can avoid the computational error effectively and can be easily performed

it has proven to be a feasible and efficacious algorithm.