Dashnic-Zusmanovich矩阵的逆的无穷范数一个新上界
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摘要
Dashnic-Zusmanovich矩阵作为一类特殊的H-矩阵在数值代数中有着重要的作用.利用矩阵逆的无穷范数,给出了Dashnic-Zusmanovich矩阵逆的无穷范数的一个新上界.通过给出的Dashnic-Zusmanovich矩阵逆的无穷范数的新上界得到了Dashnic-Zusmanovich矩阵最小奇异值新的下界,并经过比较Dashnic-Zusmanovich矩阵逆的无穷范数的新上界与已有的结果,从理论上证明了Dashnic-Zusmanovich矩阵逆的无穷范数的新上界改进了已有的结果,同时通过数值例子证明该上界改进了相关结果.
As a special class of H-matrices,the Dashnic-Zusmanovich matrix plays an important role in the numerical algebra. By using the infinite norm of the inverse of the matrix,a new upper bound of the infinite norm of the inverse of the Dashnic-Zusmanovich matrix is given. By the new upper bound of the infinite norm of the inverse of the Dashnic-Zusmanovich matrix,a new lower bound of the minimum singular value of the Dashnic-Zusmanovich matrix is obtained. By comparing the new upper bounds of the infinite norm of the inverse of the Dashnic-Zusmanovich matrix and the existing results,it is proved theoretically that the new upper bounds of the infinite norm of the inverse of the Dashnic-Zusmanovich matrix have improved the existing results, and the results are improved by numerical examples.
As a special class of H-matrices,the Dashnic-Zusmanovich matrix plays an important role in the numerical algebra. By using the infinite norm of the inverse of the matrix,a new upper bound of the infinite norm of the inverse of the Dashnic-Zusmanovich matrix is given. By the new upper bound of the infinite norm of the inverse of the Dashnic-Zusmanovich matrix,a new lower bound of the minimum singular value of the Dashnic-Zusmanovich matrix is obtained. By comparing the new upper bounds of the infinite norm of the inverse of the Dashnic-Zusmanovich matrix and the existing results,it is proved theoretically that the new upper bounds of the infinite norm of the inverse of the Dashnic-Zusmanovich matrix have improved the existing results, and the results are improved by numerical examples.
引文
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[6]ZHAO J X,LIU Q L,LI C Q,et al.Dashnic-Zusmanovich type matrices:a new subclass of nonsingular H-matrices[J].Linear Algebra&Its Applications,2018,552:277-287.
[2]李艳艳.Dashnic-Zusmanovich矩阵的逆的无穷范数上界的估计[J].西南师范大学学报(自然科学版),2017,42(6):1-4.
[3]蒋建新.块H矩阵的逆矩阵无穷范数和最小奇异值的估计[J].文山学院学报,2014,27(6):34-36.
[4]CVETKOVI C'L.H-matrixtheoryvs:eigenvalue localization[J].Numerical Algorithms,2007,42:229-245.
[5]杨占山.严格α-对角占优M-矩阵逆的无穷范数的上界估计[D].兰州:兰州大学,2011.
[6]ZHAO J X,LIU Q L,LI C Q,et al.Dashnic-Zusmanovich type matrices:a new subclass of nonsingular H-matrices[J].Linear Algebra&Its Applications,2018,552:277-287.