黎卡提方程延展解的性質及應用

Riccati Differential Equation (RDE) raises in many fields of applied Mathematics. We are particularly interested in Hermitian Riccati Differential Equation (HRDE). A solution of HRDE may blow up at isolated points. We define an extended solution for HRDE, which can be used to help the study of the convergence of a numerical algorithm. The time-asymptotic behavior of extended solutions of HRDE is investigated. The orthogonal iteration is a numerical algorithm applied to compute the invariant subspace corresponding to the r eigenvalues with largest modulus. We construct the dynamical flow ( called the orthogonal flow ) for the orthogonal iteration and study its properties. We will also derive the RDE associated with the orthogonal flow.