摘要
对标准的调和Arnoldi方法进行改进,改进后的方法在近似特征向量选取方面充分利用m步Arnoldi过程所产生的最后一个基向量vm+1的信息,在实际产生的m+1维的Krylov子空间中寻求使残量范数达到极小的调和Ritz向量作为所求的特征向量的近似.理论分析和数值实验表明了该方法的可行性和有效性.同时,将这种方法应用于图像K-L变换的协方差矩阵的特征值和特征向量的求解,能进行实时图像的压缩,较对图像分块在每个小块上进行K-L变换的方法更有效.
On the standard and Arnoldi method improvement,the improved method in the ap- proximate eigenvector selection make full use of rn step of the Arnoldi process generated by the last base vector Vm＋1 information. In the actual generated m ＋1 dimension Krylov sub- space in seeking to make the residual norm minimized harmonic Ritz vector as approximate eigenvector. Theoretical analysis and numerical experiments show that the method is feasible and effective. We apply the proposed algorithm to calculate the eigenvalue and eigenvector of covariance matrix of image for K-L transform to compress the images of real-timing. Com- pare with the dividng image into blocks and applying K-L transform on each block, the pro- posed method in this paper is more effective.
出处
《陕西科技大学学报（自然科学版）》
2012年第3期102-107,共6页
Journal of Shaanxi University of Science & Technology
