A Network Flow Analysis of Water Allocation Decisions in a River System and Their Effect on Estuarine Ecology

National Science FoundationCenter for Water and the Environmen

Erratum

Correction to the article Beightler, C. S., D. J. Wilde. 1966. Diagonalization of quadratic forms by Gauss elimination. Management Sci. 12(5, January) 371-379.

Foundations of optimization

Includes bibliographies

Diagonalization of Quadratic Forms by Gauss Elimination

The La Grange linear similarity transformation (completing the square) can be used to remove all cross-product terms from a quadratic form. It is shown that the La Grange transformation may be found conveniently by adapting the well-known Gauss elimination procedure for solving linear equations. A simple algorithm for finding the inverse transformation is given. This diagonalization scheme takes much less effort than finding the characteristic roots and vectors. It produces important simplifications in quadratic programming, statistics, and optimization problems.