1) Cauchy matrix
Cauchy矩阵
1.
For the m×n Cauchy matrix C with full column rank,the explicit expression and the fast algorithm of the minimal norm least square solution to the linear system Cx=b were indirectly obtained by construction of a special block matrix and study of the triangular decomposition of its inverse.
对于秩为n的m×n阶Cauchy矩阵C,通过构造特殊分块矩阵并研究其逆矩阵的三角分解,进而间接地得到了线性方程组Cx=b的极小范数最小二乘解的显式表达式及其快速算法,所需运算量为O(mn)+O(n2),而通常构造法方程组的方法所需运算量为O(mn2)+O(n3),用正交化法虽然避免了构造法方程组,但所需的运算量更大些。
2.
The connection between the above interpolation problem and confluent Cauchy matrix is also pointed out.
将改进后的结果推广到了多重插值指标情形 ,得到具有预先给定极点的有理函数插值问题的 Hermite型显式插值公式 ,并指出了该问题与带重点的 Cauchy矩阵的联
3.
In this paper,a fast algorithm for the Moore-Penrose inverse of an m×n Cauchy matrix with full column rank is given.
给出了求以秩为n的m×n阶Cauchy矩阵Moore-Penrose逆的快速算法,该算法的计算复杂度为O(mn)+O(n2)。
2) Cauchy matrices solution
Cauchy矩阵解
1.
Based on Cauchy matrices solutions and its interceptive Cauchy matrices solutions of homogeneous linear systems,as well as the Gronwall-Bellman inequality,some sufficient conditions of partial exponential stability are obtained for the systems and some of these results are proved to be able to guarantee different exponential convergence for parti.
利用齐次线性系统的Cauchy矩阵解、截断Cauchy矩阵解和Gronwall_Bellman不等式,得到了线性系统的解部分指数稳定确保原非线性系统的解局部部分指数稳定的充分条件,其中一些结果可以保证部分变量有不同的指数收敛率。
3) Cauchy-type matrix
Cauchy型矩阵
1.
Fast algorithm for the Moore-Penrose inverse of Cauchy-type matrix;
Cauchy型矩阵Moore-Penrose逆的快速算法
2.
For the m×n Cauchy-type matrix with full column rank,the fast algorithm of the minimal norm least square solution to the linear system Cx=b was obtained by construction of a special block matrix and study of the triangular decomposition.
对于秩为n的m×n阶Cauchy型矩阵C,通过构造特殊分块矩阵并研究其三角分解,进而得到了线性方程组C x=b的极小范数最小二乘解的快速算法,所需运算量为O(m n)+O(n2),而通常构造法方程组的方法所需运算量为O(m n2)+O(n3),用正交化法虽然避免了构造法方程组,但所需的运算量更大些。
4) generalized Cauchy matrice
广义Cauchy矩阵
1.
Using the criteria on a full row or column rank solutions of Sylvester equation, the authors discuss the full row or column rank properties of generalized Loewner matrice、Hankel matrice and generalized Cauchy matrice.
利用Sylvester方程具有行满秩或列满秩解的判定准则研究广义Loewner矩阵、Hankel矩阵和广义Cauchy矩阵的行(列)满秩性。
5) interceptive Cauchy matrix
截断Cauchy 矩阵
6) interceptive Cauchy matrices solution
截断Cauchy矩阵解
1.
Based on Cauchy matrices solutions and its interceptive Cauchy matrices solutions of homogeneous linear systems,as well as the Gronwall-Bellman inequality,some sufficient conditions of partial exponential stability are obtained for the systems and some of these results are proved to be able to guarantee different exponential convergence for parti.
利用齐次线性系统的Cauchy矩阵解、截断Cauchy矩阵解和Gronwall_Bellman不等式,得到了线性系统的解部分指数稳定确保原非线性系统的解局部部分指数稳定的充分条件,其中一些结果可以保证部分变量有不同的指数收敛率。
补充资料：Cauchy矩阵
Cauchy矩阵
Caudiy matrix
。.勿矩阵[Ca理Ilyma仕饮:R加I卫。M.lpoua]，线性常微分方程组的 确定该方程组关于空间R”(或C”)中与0和:无关的某组基的Cau由y算子(Cauchy operator)X(8，:)的矩阵.B.M.M~。H迁甲以oB撰周芝英译
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条