摘要
在隐式重新启动的广义二次Arnoldi方法中,将二次特征值问题显式投影到m维子空间中可得到2m个近似特征对,在进行隐式重新启动时会存在位移个数与子空间维数不匹配的问题.针对此困难,本文给出一种新的可使用全部位移信息的位移策略,证明该方法既能保持原方法的特殊结构,也能充分利用位移信息提高算法的效率.数值算例验证了新的位移策略通过提高每一次重新启动的效率,有效地提高了算法的整体效率.
In the implicitly restarted generalized second-order Arnoldi（GSOAR） method,we can get 2m approximate eigenpairs by projecting the quadratic eigenvalue problem（QEP） onto an m-dimensional subspace.During implicitly restarted processes,the problem is the mismatch between the number of shifts and the dimension of the subspace.In order to cure the problem,a new shift strategy for GSOAR method is proposed in this paper.We proof that the novel method can use all 2l shift candidates and preserve the special structure.Numerical experiments illustrate that the new method enhances the overall efficiency of the algorithm by increasing the efficiency of every restart process.
作者
龚方徽
孙玉泉
GONG FangHui SUN YuQuan
出处
《中国科学：数学》
CSCD
北大核心
2017年第5期635-650,共16页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:11201020)资助项目
