We　consider　numerical　methods　for　the　extreme　eigenvalue　problem　of　large　scale　symmetric　positive　definite　matrices.　By　the　variational　principle,　the　extreme　eigenvalue　can　be　obtained　by　minimizing　some　unconstrained　optimization　problem.　Firstly,　we　propose　two　adaptive　nonmonotone　Barzilai-Borwein-like　methods　for　the　unconstrained　optimization　problem.　Secondly,　we　prove　the　global　convergence　of　the　two　algorithms　under　some　conditions.　Thirdly,　we　compare　our　methods　with　eigs　and　the　power　method　for　the　standard　test　problems　from　the　UF　Sparse　Matrix　Collection.　The　primary　numerical　experiments　indicate　that　the　two　algorithms　are　promising.