一类区间矩阵特征值界的性质

Property of the Eigenvalue Bounds of a Class of Interval Matrices

对称三对角区间矩阵特征值界的计算在工程领域和力学问题中具有很重要的应用价值。证明了对满足一定条件的对称三对角区间矩阵,区间特征值的上下界必定在矩阵元素区间的端点上取到。本文的结果为计算此类对称三对角区间矩阵特征值界的方法提供了良好的判据。

The computation of bounds to eigenvalues for symmetric tridiagonal interval matrices is valuable in some mechanical and engineering problems. In this paper it is proved that the upper and lower bounds of the eigenvalues must be achieved at the end points of the interval entries for certain symmetric tridiagonal interval matrices. This provides a good criterion for computing eigenvalue bounds for the interval matrices of this type.