Inspired　by　the　successive　relaxation　method,　a　novel　discounted　iterative　adaptive　dynamic　programming　framework　is　developed,　in　which　the　iterative　value　function　sequence　possesses　an　adjustable　convergence　rate.　The　different　convergence　properties　of　the　value　function　sequence　and　the　stability　of　the　closed-loop　systems　under　the　new　discounted　value　iteration　(VI)　are　investigated.　Based　on　the　properties　of　the　given　VI　scheme,　an　accelerated　learning　algorithm　with　convergence　guarantee　is　presented.　Moreover,　the　implementations　of　the　new　VI　scheme　and　its　accelerated　learning　design　are　elaborated,　which　involve　value　function　approximation　and　policy　improvement.　A　nonlinear　fourth-order　ball-and-beam　balancing　plant　is　used　to　verify　the　performance　of　the　developed　approaches.　Compared　with　the　traditional　VI,　the　present　discounted　iterative　adaptive　critic　designs　greatly　accelerate　the　convergence　rate　of　the　value　function　and　reduce　the　computational　cost　simultaneously.