On the equivalence between matrix riccati equations and Fredholm resolvents

摘要

It is shown that the solution to every matrix Riccati equation can be generated by the resolvent of a certain Fredholm integral operator and, conversely, this resolvent can be determined from the corresponding Riccati solution. This result leads to a computational scheme, based on initial-value methods, for solving a large class of Fredholm integral equations. A connection between this theory and the factorization of integral operators is also described.