Abstract
The GMRES method is a popular iterative method for the solution of linear systems of equations with a large nonsymmetric nonsingular matrix. However, little is known about the performance of the GMRES method when the matrix of the linear system is of ill-determined rank, i.e., when the matrix has many singular values of different orders of magnitude close to the origin. Linear systems with such matrices arise, for instance, in image restoration, when the image to be restored is contaminated by noise and blur. We describe how the GMRES method can be applied to the restoration of such images. The GMRES method is compared to the conjugate gradient method applied to the normal equations associated with the given linear system of equations. The numerical examples show the GMRES method to require less computational work and to give restored images of higher quality than the conjugate gradient method.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
