Daubechies小波有限元法联系系数计算研究

摘要

针对Daubechies小波有限元法的联系系数计算精度不足这一问题,首先推导了Daubechies小波有限元法中常用联系系数的计算公式,分析了导致联系系数计算精度不足的主要原因,并首次尝试将最小二乘法引入Daubechies小波有限元法联系系数的计算中,求解所得超定方程组可得联系系数值.实例结果表明,此法可有效提高Daubechies小波有限元法联系系数的计算精度.%With the aim of solving to the problem of low computation accuracy of connection coefficients in Daubechies wavelet Finite Element Method, the calculation formulas of connection coefficients commonly used in Daubechies wavelet Finite Element Method are infered firstly, and the major cause leading to low computation accuracy of connection coefficients is analyzed. And then the least square method is employed in the computation of connection coefficients in Daubechies wavelet Finite Element Method for the first time , the values of connection coefficients can be obtained after solving the over-determined system. The results of real examples prove that this means will increase the connection coefficients' calculating accuracy in Daubechies wavelet Finite Element Method efficiently.