Abstract: We proposed a new modified three terms Hestenes-Stiefel conjugate gradient projection algorithm to solve the problems of 
large-scale nonlinear equations and signal recovery. This algorithm was constructed by a new modified three terms Hestenes-Stiefel search direction as well as a classical line search method and the hybrid plane projection technique. The new search direction automatically satisfied  sufficient descent property without any line search condition. Under conventional assumptions, the new algorthm had global convergence. Numerical results show that the new algorithm is efficient and stable.

Key words: large-scale equations, conjugate gradient method, sufficient descent property, global convergence, signal recovery