Limited Approximation of Numerical Range of Normal Matrix

Let A be an n× n normal matrix, whose numerical range NR[A] is a k -polygon. If a unit vector v ∈ W ⊆ Cn, with dimW = k and the point v∗Av ∈ IntNR[A], then NR[A] is circumscribed to NR[P∗AP], where P is an n× (k− 1) isometry of {span{v}}⊥ W → Cn, [1]. In this paper, we investigate an internal approximation of NR[A] by an increasing sequence of NR[Cs] of compressed matrices Cs = R∗s ARs, with R∗s Rs = Ik+s−1, s = 1,2, . . . ,n− k and additionally NR[A] is expressed as limit of numerical ranges of k -compressions of A. Mathematics subject classification (2000): 15A18, 15A60, 47A20.