Generalized Schultz iterative methods for the computation of outer inverses

• Published in: Computers & mathematics with applications (1987) Vol. 67; no. 10; pp. 1837 - 1847
• Main Author: Petkovic, Marko D
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-06-2014
• Subjects: Computation; Convergence; Drazin inverse; Inverse; Iterative methods; Mathematical analysis; Mathematical models; Matrices (mathematics); Moore–Penrose inverse; Outer inverse; Polynomials; Schultz method; Outer inverse; Drazin inverse; Schultz method; Moore–Penrose inverse; Iterative methods; Convergence
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2014.03.019

We consider a general matrix iterative method of the type Xk+1=Xkp(AXk) for computing an outer inverse AR(G),N(G)(2), for given matrices A∈Cm×n and G∈Cn×m such that AR(G)⊕N(G)=Cm. Here p(x) is an arbitrary polynomial of degree d. The convergence of the method is proven under certain necessary conditions and the characterization of all methods having order r is given. The obtained results provide a direct generalization of all known iterative methods of the same type. Moreover, we introduce one new method and show a procedure how to improve the convergence order of existing methods. This procedure is demonstrated on one concrete method and the improvement is confirmed by numerical examples.