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.
Several optimization procedures have been proposed for the analysis of complex water resource planning problems. One of these techniques, dynamic programming, has been limited in its applicability to river basin systems, because these systems are nonserial and dynamic programming is by nature a serial procedure. Recently developed methods are discussed and illustrated with example problems for decomposing the nonserial river basin system into equivalent serial systems amenable to analysis by the dynamic programming method.
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