Kernel　ridge　regression　is　an　important　nonparametric　method　for　estimating　smooth　functions.　We　introduce　a　new　set　of　conditions　under　which　the　actual　rates　of　convergence　of　the　kernel　ridge　regression　estimator　under　both　the　L-2　norm　and　the　norm　of　the　reproducing　kernel　Hilbert　space　exceed　the　standard　minimax　rates.　An　application　of　this　theory　leads　to　a　new　understanding　of　the　Kennedy-O＇Hagan　approach　[J.　R.　Stat.　Soc.　Ser.　B.　Stat.　Methodol.,　63　(2001),　pp.　425-464]　for　calibrating　model　parameters　of　computer　simulation.　We　prove　that,　under　certain　conditions,　the　Kennedy-O＇Hagan　calibration　estimator　with　a　known　covariance　function　converges　to　the　minimizer　of　the　norm　of　the　residual　function　in　the　reproducing　kernel　Hilbert　space.