摘要
通过举例,指出了给定的Minkowski型不等式的两处错误,并从理论上分析了该错误产生的原因。在此基础上,结合H矩阵的特点,运用特征值分布、不等式运算等方法,补充了结论成立的必要条件,修正了H矩阵的该Minkowski型不等式的不足之处,并将结论加以推广;其次,通过进一步的分析,对H矩阵的另一个不等式作了推广。这种对原有结论的修正和推广,不仅丰富和充实了H矩阵理论本身,对生物学、计算数学等相关领域内容的发展也奠定了理论基础。
First, two mistakes about the Minkowski inequality of H--matrix were pointed by practical examples and reason of the mistakes was found on a view of theory analysis. On the base, some necessary conditions were improved and Minkowski inequality was further modified by considering H--matrix properties, using eigenvalues＇ distribution, inequality＇s calculation and other methods,and the corresponding results were generalized. Second, another important inequality of H--matrix was also generalized by the analysis of the Minkowski inequality. The modify and generalization not only offer supports to the H-- matrix theory itself, but also do good to development of biology, computers and mathematics and other related fields.
出处
《辽宁石油化工大学学报》
CAS
2008年第1期81-85,共5页
Journal of Liaoning Petrochemical University
基金
辽宁省教育厅高校科研项目(2004F100)
关键词
H矩阵
特征值
不等式
H--matrix
Eigenvalues
Inequality
