A constrained eigenvalue problem
Walter Gander, Gene Howard Golub, U. von Matt · Repository for Publications and Research Data (ETH Zurich) · 1988
In this paper we consider the following mathematical and computational problem. Given the quantities A: (n + m)-by-(n + m) matrix, symmetric, n > 0 N: (n + m)-by-m matrix with full rank t: vector of dimension m with ∥(NT)+t∥ < 1 Determine an x such that $$ {\operatorname{x} ^T}Ax = \min $$ subject to the constraints $$ {N^T}x = t $$ (i) $$ {x^T}x = 1. $$ (ii) Variants of this problem occur in many applications [1,5,7,8,11]. The problem has been studied previously when t = 0, the null vector, (cf. [4,6]). When t ≠ 0, then the problem becomes more complicated.