It is shown that, if algorithms for performing the QR decomposition are free from calculation of square root, the related iterative refinement algorithms can also be square root free.

Also, estimates of the regression coefficients can sometimes be improved through iterative refinement.

In combination with dynamic balance practice,we deal with some problems existing in the influence coefficient method,for example,excessive hangover vibration and inadequate balance weighted mass match,and propose the following three ameliorative methods: weighted iteration least-squares method,restrained mass match least-squares method and genetic algorithm-based least-squares method.

The acceleration method is discussed,the convergence is proved and the error estimation is given.

One dimension iteration encryption-recognition of image;