CAJ | 학술논문

非奇异H-矩阵在控制理论、科学计算和工程应用中具有重要的作用，但在实际中要判定一给定矩阵为非奇异H-矩阵是有难度的。本文通过研究给定矩阵元素的性质，对矩阵元素的航标集进行分割，巧妙地构造正对角矩阵和运用不等式的放缩方法，给出了非奇异H-矩阵的一组新的实用性新判定方法。进一步，将相关结果推广到不可约和具有非零元素链的情形。最后，我们改进和推广了相关的结果，并举例说明了所得方法的优越性。
비기이H-구진재공제이론、과학계산화공정응용중구유중요적작용，단재실제중요판정일급정구진위비기이H-구진시유난도적。본문통과연구급정구진원소적성질，대구진원소적항표집진행분할，교묘지구조정대각구진화운용불등식적방축방법，급출료비기이H-구진적일조신적실용성신판정방법。진일보，장상관결과추엄도불가약화구유비령원소련적정형。최후，아문개진화추엄료상관적결과，병거례설명료소득방법적우월성。
Nonsingular H-matrix plays a significant role in the control theory, the scientific computation and the applications in engineering. However, it is di?cult to specify a non-singular H-matrix in practice. In this paper, we partition the row index set by studying the elements of a matrix, and construct a positive diagonal matrix. Then, we apply some tech-niques in inequalities to obtain a new criterion for nonsingular H-matrices. We also obtain several similar results in the cases of irreducible matrices and matrices with non-zero elements chains. These consequences improve and generalize the related results, and the advantage of the proposed consequences are illustrated by several numerical examples.