Institution: Stanford University, Department of Computer Science

Title: Maximizing a second-degree polynomial on the unit sphere

Author: Forsythe, George E.

Author: Golub, Gene H.

Date: February 1965

Abstract: Let A be a hermitian matrix of order n, and b a known vector in $C^n$. The problem is to determine which vectors make $\Phi (x) = {(x-b)}^H\ A(x-b)$ a maximum or minimum on the unit sphere U = {x : $x^H$x = 1}. The problem is reduced to the determination of a finite point set, the spectrum of (A,b). The theory reduces to the usual theory of hermitian forms when b = 0.

http://i.stanford.edu/pub/cstr/reports/cs/tr/65/16/CS-TR-65-16.pdf