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In this research, a modified hybrid Dai-Yuan and Hestenes-Stiefel (DYHS) conjugate gradient (CG) algorithm is presented, with develops sufficient descent property. The hyperplane projection method is also used and the algorithm is a convex combination of DY and HS parameters. With some reasonable assumptions, the global convergence property is obtained under accelerated step size. The numerical experiment demonstrate that the DYHS algorithm is more effective and robust than other existing methods for solving nonlinear monotone equations and signal recovery problems. Mathematics Subject Classification: 65K05, 90C52, 90C26

In this paper, we propose a solution method via hybrid spectral conjugate gradient and signal recovery problem (ANHSCG) to solve nonlinear monotone equations. This has been done using the hybrid conjugate gradient (CG) parameters of Dai-Yuan (DY), conjugate descent (CD), Hestenes-Stiefel (HS), Liu-Storey (LS) and the corresponding search direction of spectral conjugate gradient method. The search direction has proved to be adequately descent regardless of the step-size. Under reasonable assumptions, the convergence of the algorithm is established. Additionally, numerical tests are run on a set of benchmark test problems to illustrate the effectiveness and competitiveness of the new algorithm compared with other existing alternatives. Finally, some applications of the proposed algorithm is explored. Mathematics Subject Classification: 65K05, 90C52, 90C26