Using a limit process, it is proved in this paper that the adjoint matrix of an idempotent matrix is idempotent and the adjoint matrix of a nilpotent matrix is also nilpotent. The results are richer than that in [1].
Adjoint-free calculation method is proposed to compute conditional nonlinear optimal perturbations(CNOP) combined with initial perturbations and model parameter perturbations. The new approach avoids the use of adjoin...Adjoint-free calculation method is proposed to compute conditional nonlinear optimal perturbations(CNOP) combined with initial perturbations and model parameter perturbations. The new approach avoids the use of adjoint technique in the optimization process. CNOPs respectively generated by ensemble-based and adjoint-based methods are compared based on a simple theoretical model.展开更多
文摘Using a limit process, it is proved in this paper that the adjoint matrix of an idempotent matrix is idempotent and the adjoint matrix of a nilpotent matrix is also nilpotent. The results are richer than that in [1].
基金supported by National Natural Science Foundation of China(Grant No.11201265)Shandong Natural Science Foundation(Grant No.ZR2012AM003)China Postdoctoral Science Foundation(Grant No.20110490564)
文摘Adjoint-free calculation method is proposed to compute conditional nonlinear optimal perturbations(CNOP) combined with initial perturbations and model parameter perturbations. The new approach avoids the use of adjoint technique in the optimization process. CNOPs respectively generated by ensemble-based and adjoint-based methods are compared based on a simple theoretical model.
