On the equivalence between matrix riccati equations and Fredholm resolvents

✍ Scribed by Alan Schumitzky

• Publisher: Elsevier Science
• Year: 1968
• Tongue: English
• Weight: 393 KB
• Volume: 2
• Category: Article
• ISSN: 0022-0000
• DOI: 10.1016/s0022-0000(68)80005-4

✦ Synopsis

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.