In this paper, the EPE_k method is considered and the positive-definable matrix isdefined. The results of this paper can also be applied to other iterative method.
本文在A为H阵的情况下给出了一个较前人给出的更为简单和具体的‖A^(-1)‖_x的上界,本文还定义了“等对角优势矩阵”,并证明了若A为具有等对角优势δ的等对角优势矩阵(亦即|α_(ij)|-sum from i≠1 to(|α_(ij)|)=δ,(?)_i),则P(A^(-1))...本文在A为H阵的情况下给出了一个较前人给出的更为简单和具体的‖A^(-1)‖_x的上界,本文还定义了“等对角优势矩阵”,并证明了若A为具有等对角优势δ的等对角优势矩阵(亦即|α_(ij)|-sum from i≠1 to(|α_(ij)|)=δ,(?)_i),则P(A^(-1))=‖A^(-1)‖_x=sum from j to(A^(-1))_(ij)=1/δ,(?)_i,利用等对角优势M阵,可以求任何H阵A的‖A^(-1)‖_x的上界,最后我们还给出了几个有趣的例子以说明本文的一些定理。展开更多
In this papert the matrix of equidiagonal-dominance is defined and several theorems about ||A-1||∞ and its evaluation are established. Many interesting numerical examples are given.
文摘In this paper, the EPE_k method is considered and the positive-definable matrix isdefined. The results of this paper can also be applied to other iterative method.
文摘本文在A为H阵的情况下给出了一个较前人给出的更为简单和具体的‖A^(-1)‖_x的上界,本文还定义了“等对角优势矩阵”,并证明了若A为具有等对角优势δ的等对角优势矩阵(亦即|α_(ij)|-sum from i≠1 to(|α_(ij)|)=δ,(?)_i),则P(A^(-1))=‖A^(-1)‖_x=sum from j to(A^(-1))_(ij)=1/δ,(?)_i,利用等对角优势M阵,可以求任何H阵A的‖A^(-1)‖_x的上界,最后我们还给出了几个有趣的例子以说明本文的一些定理。
文摘In this papert the matrix of equidiagonal-dominance is defined and several theorems about ||A-1||∞ and its evaluation are established. Many interesting numerical examples are given.
