论文标题
有限的内存多项式方法用于大规模矩阵函数
Limited-memory polynomial methods for large-scale matrix functions
论文作者
论文摘要
矩阵函数是线性代数的核心主题，在科学计算中，需要其数值近似的问题越来越经常出现。我们回顾了各种有限记忆方法，以近似大规模矩阵函数在向量上的作用。重点是多项式方法，其记忆要求是已知或处方的。详细处理了基于显式多项式近似或插值以及重新启动的Arnoldi方法的方法。还提供了现有软件的概述，以及关于具有挑战性的开放问题的讨论。
Matrix functions are a central topic of linear algebra, and problems requiring their numerical approximation appear increasingly often in scientific computing. We review various limited-memory methods for the approximation of the action of a large-scale matrix function on a vector. Emphasis is put on polynomial methods, whose memory requirements are known or prescribed a priori. Methods based on explicit polynomial approximation or interpolation, as well as restarted Arnoldi methods, are treated in detail. An overview of existing software is also given, as well as a discussion of challenging open problems.
