强奇异积分方程小波Petrov-Galerkin快速算法

Fast Wavelet Petrov-Galerkin Methods for Singular Integral Equations

通过构造具有高阶消失矩、小支集和半双正交性质的分片多尺度小波基底,给出第2类强奇异积分方程的小波Petrov-Galerk in快速算法,并证明该算法收敛阶达到最佳,条件数有界,计算复杂性几乎最佳。

Two suitable muhiscale wavelet bases are constructed, which have the higher vanishing moment, small support and bi-orthogonal properties. Using this bases, fast Petrov-Galerkin methods are developed, and are shown having optimal order of convergence, almost optimal complexity and bounded condition number.