SYMMETRICAL QUASIDEFINITE MATRICES

It is stated here that a symmetric matrix K is quasidefinite if it has the form [GRAPHICS], where E and F are symmetric positive definite ma trices. Although such matrices are indefinite, it is shown that any sy mmetric permutation of a quasidefinite matrix yields a factorization L DL(T). This result is applied to obtain a new approach for solving the symmetric indefinite systems arising in interior-point methods for li near and quadratic programming. These systems are typically solved eit her by reducing to a positive definite system or by performing a Bunch -Parlett factorization of the full indefinite system at every iteratio n. This is an intermediate approach based on reducing to a quasidefini te system. This approach entails less fill-in than further reducing to a positive definite system, but is based on a static ordering and is therefore more efficient than performing Bunch-Parlett factorizations of the original indefinite system.