Generalized Schultz iterative methods for the computation of outer inverses

作者：Petkovic Marko D^*

来源：Computers & Mathematics with Applications, 2014, 67(10): 1837-1847.

DOI：10.1016/j.camwa.2014.03.019

• Moore-Penrose inverse
• Drazin inverse
• Outer inverse
• Iterative methods
• Convergence
• Schultz method

We consider a general matrix iterative method of the type Xk+1 = X(k)p(AX(k)) for computing an outer inverse A(R(G),N(G))((2)), for given matrices A is an element of C-mxn and G is an element of C-nxm such that AR(G) circle plus N(G) = C-m. 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.

• 出版日期2014-6