Generalized inverse eigenvalue problem for matrices whose graph is a path

In this paper, we analyse a special generalized inverse eigenvalue problem A(n)x = lambda B(n)x for the pair (A(n), B-n) of matrices each of whose graph is a path on n vertices, by investigating the leading principal minors of the matrix A(n) - lambda B-n. From the given data consisting of B-n, a matrix A(k) (k < n) whose graph is a path on k vertices, two column vectors X-2, Y-2 is an element of Rn-k and distinct real numbers lambda and mu we construct A(n) and two column vectors X-1, Y-1 is an element of R-k such that A(k) is the leading principal sub-matrix of A(n) and (lambda, X), (mu, Y) are the eigenpairs of (A(n), B-n), where X = (X-1(T), X-2(T))(T) and Y = (Y-1(T), Y-2(T))(T) Further, numerical examples are also given to demonstrate the applicability of the results developed here. (C) 2014 Elsevier Inc. All rights reserved.