Orthogonal polynomials and semi-iterative methods for the Drazin-inverse solution of singular linear systems
The authors present a novel class of semi-iterative methods for the Drazin-inverse solution of consistent and inconsistent singular linear systems. The coefficient matrices of the studied systems of equations are allowed to have arbitrary index and arbitrary spectra in the complex plane. Short review of semi-iterative methods for the Drazin-inverse solution of singular linear systems is presented. The methods and algorithms, which are reported, are based on orthogonal polynomials and can be implemented by four-term recursion relations independently of the index. All the computational details of the algorithms and a complete convergence analysis for the methods are given. The use of the new algorithms and the convergence theory developed is illustrated with a simple numerical example.
scientific article; zbMATH DE number 1884036