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

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...

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,...

On Squaring Krylov Subspace Iterative Methods for Nonsymmetric Linear Systems

The Biorthogonal Lanczos and the Biconjugate Gradients methods have been proposed as iterative methods to approximate the solution of nonsymmetric and indefinite linear systems. Sonneveld [19] obtained the Conjugate Gradient Squared by squaring the matrix polynomials of the Biconjugate Gra­ dients method. Here we square the Biorthogonal Lanczos, the Biconjugate Residual and the Biconjugate Orth...

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