A QMR-Type Algorithm for Drazin-Inverse Solution of Singular Nonsymmetric Linear Systems

DGMRES: A GMRES-type algorithm for Drazin-inverse solution of singular nonsymmetric linear systems

In a recent work by the author [Linear Algebra Appl. 298 (1999) 99] Krylov subspace methods were derived for the Drazin-inverse solution of consistent or inconsistent linear systems of the form Ax = b, where A ∈ CN×N is a singular and in general non-hermitian matrix that has an arbitrary index. One of these methods, modeled after the generalized conjugate residual method (GCR) and denoted DGCR,...

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

A unified approach to Krylov subspace methods for the Drazin-inverse solution of singular nonsymmetric linear systems

Consider the linear system Ax = b, where A ∈ CN×N is a singular matrix. In the present work we propose a general framework within which Krylov subspace methods for Drazininverse solution of this system can be derived in a convenient way. The Krylov subspace methods known to us to date treat only the cases in which A is hermitian and its index ind(A) is unity necessarily. In the present work A i...

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...

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...