IGMRES method for linear systems

Document Type : Research Paper

Author

Department of Applied Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran.

Abstract

The Index Generalized Minimal RESidual (IGMRES) algorithm is designed to compute the Drazin-inverse solution of a linear system of equations $Ax=b$, where $A$ is an arbitrary square matrix with index $\gamma$. If $\gamma=0$, then the this method method coincide with Generalized Minimal RESidual (GMRES) method. Also, the {$k^{th}$} ideal index generalized minimal residual polynomial of $A$ is introduced and the roots of these polynomials are studied. Moreover, by numerical results the convergence rate of these methods are compared by two examples.

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References

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History

  • Receive Date: 16 September 2023
  • Revise Date: 20 February 2024
  • Accept Date: 13 March 2024

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