The GMRES method is a popular iterative method for the solution of large linear systems of equations with a nonsymmetric nonsingular matrix.
The CGNR method is a popular iterative method for the solution of large linear systems of equations with a general matrix. When equipped with a suitable stopping rule, both GMRES and CGNR are regularization methods for the solution of linear ill-posed problems. In this talk we describe modifications of the GMRES and CGNR methods which make them suitable for computing nonnegative solutions of linear ill-posed problems.
Several computed examples illustrate that the nonnegative restarted GMRES and CGNR method can computed nonnegative solution of better quality and at lower computational cost than other algorithms for the nonnegative solution of
ill-posed problems proposed in the literature.
This talk presents joint work with G. Landi, L. Reichel and F. Sgallari
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