A Fast Collocation Method for Eigen-Problems of Weakly Singular Integral Operators

作者：Chen, Zhongying; Nelakanti, Gnaneshwar; Xu, Yuesheng^*; Zhang, Yongdong

来源：Journal of Scientific Computing, 2009, 41(2): 256-272.

DOI：10.1007/s10915-009-9295-z

• Fast collocation method
• Compact integral operator
• Multiscale interpolation
• Eigen-problem

A multiscale collocation method is developed for solving the eigen-problem of weakly singular integral operators. We employ a matrix truncation strategy of Chen, Micchelli and Xu to compress the collocation matrix, which the compressed matrix has only O(N log N) nonzero entries, where N denotes the order of the matrix. This truncation leads to a fast collocation method for solving the eigen-problem. We prove that the fast collocation method has the optimal convergence order for approximation of the eigenvalues and eigenvectors. The power iteration method is used for solving the corresponding discrete eigen-problem. We present a numerical example to demonstrate how the methods can be used to compute a nonzero eigenvalue rapidly and efficiently.

• 出版日期2009-11
• 单位中山大学