广义严格α-链对角占优矩阵新的判定准则

摘要

广义严格对角占优矩阵在数学、系统理论、弹性力学及经济学等诸多领域有着广泛的应用，但如何在实际应用中简便地判别一个矩阵是否是广义严格对角占优矩阵一直是人们关注的问题。本文通过α-链对角占优矩阵的性质，巧妙的把不等式关系转化并构造出相应的正对角阵矩阵，给出了广义严格α-链对角占优矩阵的一种新的判定准则，改进了近期的相关结果，并用数值算例说明了该算法的有效性。%Generalized strictly diagonally dominant matrices plays a very significant role in numerical analysis and matrix theory, and has a wide range of applications in mathematics, systematic theory, elasticity and economics, etc. How to specify a generalized strictly diago-nally dominant matrices in practice has always been paid attention. In the paper, some new determinate codes for generalized strictly α-chain diagonally dominant matrices are obtained according to the properties ofα-chain diagonally dominant matrices, transforming the inequal-ity relationship and constructing a positive diagonal matrix skillfully. The related results are improved. Effectiveness of the new codes is illustrated by some numerical examples.