Point Exchange Algorithm In Wavelet Analysis

This paper mainly study the method of using polynomials p(y) to approx-imate the continuous function 1/y in closed interval [a ,1](a> 0). Firstly, we introduce the theoretical content of one-point exchange algorithm and the re-alization of it by MATLAB, comparing the approximation effect between the exchange algorithm and other methods. We then illustrate that the one-point algorithm is much better for particular examples. But this method of approxi-mation is not from one side. We wish to find a better one which reserves not only the approximation effect of exchange algorithm, but also the good property of approximating from one side. However, we can't improve the exchange algorithm if we observe and analysis it more deeply. So we turn to other methods with sim-plest polynomials.By calculation, we provide a new algorithm 2.1.4.1 which is different from theorem 1.1 and compare the approximation effect between algo-rithm 2.1.4.1 and theorem 1.1.