【摘要】 利用一个稀疏矩阵来代替稠密的系数矩阵的方法,构造了紧积分算子特征值问题的快速谱算法.通过选择傅里叶基底,建立了快速Fourier-Galerkin算法,并证明了该算法具有最佳收敛阶.同时,证明了压缩矩阵非零项的最优复杂度仅为O(nlog n),其中2n+1表示矩阵的阶.更多还原

【Abstract】 We propose a fast spectral method for eigen-problems of compact integral operators by using a sparse matrix to approximate the obtained dense coefficient matrix.Choosing Fourier basis,we establish a fast Fourier-Galerkin method and show that this method has an optimal convergence order which is the same as noncompression method,and has optimal complexity with only O(n log n)nonzero entries in the compressed matrix,where 2n+1 denotes the order of the matrix.更多还原