Extreme Spectra Realization by Nonsymmetric Tridiagonal and Nonsymmetric Arrow Matrices

H. Pickmann-Soto, S. Arela-Pérez, Juan C. Egaña, Ricardo L. Soto
2019 Mathematical Problems in Engineering  
We consider the following inverse extreme eigenvalue problem: given the real numbers {λ1j,λjj}j=1n and the real vector x(n)=x1,x2,...,xn, to construct a nonsymmetric tridiagonal matrix and a nonsymmetric arrow matrix such that {λ1j,λjj}j=1n are the minimal and the maximal eigenvalues of each one of their leading principal submatrices, and x(n),λn(n) is an eigenpair of the matrix. We give sufficient conditions for the existence of such matrices. Moreover our results generate an algorithmic procedure to compute a unique solution matrix.
doi:10.1155/2019/3459017 fatcat:6m6szogfwffvhmfcajw4zxj46m