第三类和第四类Chebyshev小波积分算子矩阵及其在数值积分中的应用

Integral Operator Matrices of the Third and Fourth Kinds Chebyshev Wavelets and the Application on Numerical Integrations

本文给出第三类和第四类Chebyshev小波的积分算子矩阵,研究Chebyshev小波展开的一致收敛性和系数估计.基于第三类和第四类Chebyshev小波积分算子矩阵,将定积分和双重积分转化成矩阵运算,得到计算定积分和双重积分近似值的一种算法.数值算例表明此方法的可行性和有效性.

In this paper, the integral operator matrices of the third and fourth kinds Chebyshev wavelets axe derived. The uniform convergence analysis and coefficients estimation for the Chebyshev expansion of a function are given. An algorithm is developed to obtain approximate values of definite integrals as well as double integrals by using the third and fourth kinds Chebyshev wavelets. Definite integral is transformed into matrix operation by combining the third and fourth kinds Chebyshev wavelets with integral operator matrices. Some examples are provided to demonstrate the feasibility and efficiency of the proposed method.