ON THE RELATIONSHIP BETWEEN THE EIGENVALUES OF TRIDIAGONAL MATRIX AND OF ITS SUBMATRICES
Mu D · 1986
Suppose tridiagonal matrixthree problems will be considered in this paper: (1) Estimate the upper bound forwhere μi are the eigenvalues of Bn and λ is a fixed eigenvalue of a principal subma-trix Bl of Bn(1≤Zn).(2) Estimate the upper bound for the spectral variation SBn (Bl) of Bl with respect to Bn:SBn (Bl) = max min| μi-λj| 1≤j≤l 1≤i≤nand the eigenvalue variation VBn (Bl) of Bl with respect to Bn:VBn (Bl) = min max | μx(i)-λj| x 1≤j≤lwhere the minimum is taken with respect to the set or, all permutations of (1, 2, ... , n).(3) Consider the stability of dl(λ), SBn(Bl),VBn(Bl)