Institution: Stanford University, Department of Computer Science

Title: Stationary values of the ratio of quadratic forms subject to linear constraints

Author: Golub, Gene H.

Author: Underwood, Richard R.

Date: November 1969

Abstract: Let A be a real symmetric matrix of order n, B a real symmetric positive definite matrix of order n, and C an n$\times$p matrix of rank r with r $\leq$ p < n. We wish to determine vectors $\underset ~\to x$ for which ${\underset ~\to x}^T\ A\underset ~\to x\ / {\underset ~\to x}^T\ B\underset ~\to x$ is stationary and $C^T \underset ~\to x\ = \underset ~\to \Theta$, the null vector. An algorithm is given for generating a symmetric eigensystem whose eigenvalues are the stationary values and for determining the vectors $\underset ~\to x$. Several Algol procedures are included.

http://i.stanford.edu/pub/cstr/reports/cs/tr/69/142/CS-TR-69-142.pdf