Wavelet Galerkin method for eigenvalue problem of a compact integral operator

作者：Panigrahi Bijaya Laxmi^*; Nelakanti Gnaneshwar

来源：Applied Mathematics and Computation, 2011, 218(4): 1222-1232.

DOI：10.1016/j.amc.2011.05.114

• Convergence rates
• Wavelet basis
• Eigenvalue problem
• Integral equations
• Compact operator

We consider the approximation of eigenfunctions of a compact integral operator with a smooth kernel by the Galerkin method using wavelet bases. By truncating the Galerkin operator, we obtain a sparse representation of a matrix eigenvalue problem. We prove that the error bounds for the eigenvalues and for the distance between the spectral subspaces are of the orders O(n mu(-2nr)) and O(mu(-nr)), respectively, where mu(-n) denotes the norm of the partition and r denotes the order of the wavelet basis functions. By iterating the eigenvectors, we show that the error bounds for the eigenvectors are of the order O(nl(-2nr)). We illustrate our results with numerical results.

• 出版日期2011-10-15