一类Toeplitz线性代数方程组的预处理GMRES方法

本文研究一类来源于分数阶特征值问题的Toeplitz线性代数方程组的求解.构造Strang循环矩阵作为预处理矩阵来求解该Toeplitz线性代数方程组,分析了预处理后系数矩阵的特征值性质.提出求解该线性代数方程组的预处理广义极小残量法（PGMRES）,并给出该算法的计算量.数值算例表明了该方法的有效性.     

Existence of Some Specific Elements in Finite Fields北大核心CSCD

Let q = pk and Fqn be the extension field of Fq of degree n, where p is an odd prime and n, k are positive integers. The main contribution of this paper is as follows: If n | (q − 1), k ≥ 11, n ≥ 14 or n (q − 1), k ≥ 10, n ≥ 8, then there exists a primitive element α in Fqn such that α + α−1 is a normal element, and 1 + α2 is a square element, and there exists a normal element β, such that β + β−1 is a primitive element, and 1 + β2 is a square element. © 2022 Chinese Academy of Sciences. All rights reserved.