Development of iterative techniques and extrapolation methods for Drazin inverse solution of consistent or inconsistent singular linear systems

Development of Iterative Techniques and Extrapolation Methods for Drazin Inverse Solution of Consistent or Inconsistent Singular Linear Systems

Consider the linear system of equations Bx =f, where B is an N x N singular matrix. In an earlier work by the author it was shown that iterative techniques coupled with standard vector extrapolation methods can be used to obtain or approximate a solution of this system when it is consistent. In the present work we expand on that approach to treat the case in which this system is in general inco...

DEVELOPMENT OF NEW ITERATIVE TECHNIQUES AND EXTRAPOLAnON METHODS FOR CONSISTENT OR INCONSISTENT SINGULAR LINEAR SYSTEMS

Consider the linear system of equations Bx=f , where B is an N xN singular matrix. In an earlier work [5] by the author it was shown that iterative techniques coupled with standard vector extrapolation methods can be used to obtain (approximations to) a solution of this sys­ tem when it is consistent. In the present work we expand on the approach of [5] to treat the case in which this system is...

Orthogonal polynomials and semi-iterative methods for the Drazin-inverse solution of singular linear systems

In this work we present a novel class of semi-iterative methods for theDrazin-inverse solution of singular linear systems,whether consistent or inconsistent. The matrices of these systems are allowed to have arbitrary index and arbitrary spectra in the complex plane. The methods we develop are based on orthogonal polynomials and can all be implemented by 4-term recursion relations independently...

A Bi-CG type iterative method for Drazin-inverse solution of singular inconsistent nonsymmetric linear systems of arbitrary index

Application of Vector Extrapolation Methods to Consistent Singular Linear Systems

Consider the linear system of equations Bx = f, where B is an N x N singular matrix, but the system is consistent. In this work we show that iterative techniques coupled with vector extrapolation methods can be used to obtain (approximations to) a solution of Bx = f. We do this by extending the results of some previous work on vector extrapolation methods as they apply to nonsingular matrices B...