Schur techniques in invariant imbedding methods for solving two-point boundary value problems

Schur-type techniques for the solution of various types of Riccati equations by means of associated generalized eigenvalue/eigenvector problems are discussed. In the case of symmetric Riccati equations various aspects of an associated generalized Hamiltonian or symplectic structure are considered. The same generalized eigenvalue/eigenvector methodology carries through to the solution of nonsymmetric Riccati equations and is illustrated by application to invariant imbedding methods for solving two-point boundary value problems. Implicit differential equation problems are shown to give rise to "generalized" Riccati equations in both the symmetric and nonsymmetric case.