Schur parametrization of symmetric indefinite matrices
It is shown that the generalized Schur algorithm for triangular factorization of symmetric positive definite matrices has a natural extension to the factorization of symmetric indefinite matrices with nonsingular principal submatrices. The proof is constructive and provides for an explicit formulation of the J-orthogonal and triangular matrices involved in the procedure. The (group-theoretic) significance of degenerate transformation steps involving unbounded reflection coefficients is precisely identified. It is found how to assign them an interpretation as Schur parameters and how to get benefit from this knowledge for performing a suitable change of equivalence class during execution, instead of a breakdown of the algorithm.<<ETX>>