Another Hager-Zhang-type method via singular-value study for constrained monotone equations with application

Without setting any condition on the parameter θ_k of a four-term version of the classical one-parameter Hager-Zhang (HZ) method, this article proposes another HZ-type scheme for solving constrained monotone equations, where the condition for global convergence is satisfied for θ_k∈[0,+∞). This is an improvement from the former, its recent adaptive variant, where the global convergence condition holds for θ_k∈(0,+∞) under certain defined condition, as well as other adaptations for systems of monotone equations, where the condition holds only when θ_k∈(14,+∞). By conducting singular value study of iteration matrix of the scheme, a choice of θ_k restricted in the interval (0,14] is obtained to study its impact on the scheme. Moreover, the scheme converges globally and its effectiveness is shown by some numerical experiments and image de-blurring application.