大规模矩阵函数的有限记忆多项式方法
Limited-memory polynomial methods for large-scale matrix functions
摘要：
矩阵函数是线性代数的一个中心课题，在科学计算中，要求其数值逼近的问题越来越多地出现。我们回顾了各种有限记忆的方法，一个大规模的矩阵函数对向量的作用的近似。重点放在多项式的方法，其内存要求是已知的或规定的先验。方法的基础上明确的多项式逼近或插值，以及重新启动Arnoldi方法，详细处理。现有的软件的概述，以及具有挑战性的开放问题的讨论。
英文摘要：
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.
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