Different Tikhonov RegularizationOperators for Elementary ResidualMethod
Keywords:
Elementary Residual; Hessenberg Decomposition; Ill-Posed Linear Systems; Regularization Techniques; Tikhonov Regularization.Abstract
ELeMentary RESidual (ELMRES) method is a recently proposed krylov subspace method, which
its implementation is similar to GMRES; however this does not use any Arnoldi orthogonalization technique.
The implementation of ELMRES is based on Hessenberg decomposition. The main aim of this work is to solve
(nearly) singular linear system of equations by ELMRES using Tkhonov regularization. But, the more
important issue is that we collect several different appropriate sets of Tikhonov regularization parameters for
ELMRES and compare the performances of these operators by some popular numerical tests to find some more
practical class of Tikhonov operators for this iterative method. Therefore, some numerical experiments, which
compare the performances of these operators, as well as conclusion, are drawn at the end of this work.
