Theory And Method Of Generalized Inverse Function-Valued Padé Approximation And Its Applications In Fredholm Integral Equations

On the basis of the works of Graves-Morris, this paper obtain the following primary results:1. Generalized inverse real function-valued Padé approximation (GFPA) is extended to the case of complex function-value, and then a new definiton of generalized inverse complex function-valued Padé approximation (CGFPA) is defined.2. An intact detenninantal formula of CGFPA is constructed, and its Pfaffian reduced formula is given. Existence and uniqueness of CGFPA are proved by means of the determinant form.3. A new complex generalized inverse is defined by L2(R) normal formula:and then three efficient recursive algorithms to compute CGFPA and Wynn identity are established.4. According to Hermite formula of CGFPA, well-known De Montessus - De Ballore convergence theorem is proved. Some algebraic properties of CGFPA are presented.5. Some integral equations are given to show the determinantal formula and recursive algorithms of CGFPA.