隐式重新启动精化Lanczos双对角化方法  

An Implicitly Restarted Lanczos Bidiagonalization Method with Refined Vector

作　　者：赖降周[1] 卢琳璋[1] 

机构地区：[1]厦门大学数学科学学院福建,厦门361005

出　　处：《厦门大学学报（自然科学版）》2009年第2期153-159,共7页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(10531080)资助

摘　　要：给出一种计算少数几个最小奇异三元组的隐式重新启动精化Lanczos双对角化方法,采用调和Ritz值作为位移,有效地逼近大规模矩阵的小奇异值的奇异三元组.算法用精化残量,精化奇异向量和精化Rayleigh商,同时采取压缩技术压缩掉已经求出的小的奇异三元组.数值实验表明,算法更有效地求解大规模矩阵的小奇异三元组,收敛速度也快.An implicitly restarted Lanczos bidigonalization method with refined vector for computing smallest singular triplets is developed. The harmonic Ritz are used as the shift and small singular triplets can be got more efficiently. Refined singular vector,the refined residual, refined Rayleigh equotient and the deflation technique are also used. Numerical experiments had been given to confirm that the algorithm is more efficient and it converges rather fast.

关 键 词：Lanczos双对角化 RITZ值 调和Ritz值 正交压缩变换 精化奇异向量 精化残量 

分 类 号：O241.6[理学—计算数学]