向量范数与矩阵范数的相容性研究

Study on Compatibility between Vector Norms and Matrix Norms

针对范数理论在研究算法的收敛性、稳定性以及误差分析中的重要应用,从向量范数出发,引入矩阵范数,进一步讨论向量范数与矩阵范数的相容性问题,给出了求与向量范数相容的矩阵范数的方法,并得出算子范数即为与向量范数相容的矩阵范数。

in view of the important application of norm theory in the study of convergence,stability and error analysis of the algorithm,the matrix norm is introduced from the vector norm to further discuss the compatibility the vector norm and the matrix norm is further discussed.The method of finding matrix norm compatible with vec⁃tor norm is given,and the operator norm is the matrix norm compatible with vector norm.