This paper deals with Hermite learning which aims at obtaining the target function from the samples of function values and the gradient values. Error analysis is conducted for these algorithms by means of approaches f...This paper deals with Hermite learning which aims at obtaining the target function from the samples of function values and the gradient values. Error analysis is conducted for these algorithms by means of approaches from convex analysis in the frame- work of multi-task vector learning and the improved learning rates are derived.展开更多
Nonlinear fastest growing perturbation, which is related to the nonlinear singular vector and nonlinear singular value proposed by the first author recently, is obtained by numerical approach for the two-dimensional q...Nonlinear fastest growing perturbation, which is related to the nonlinear singular vector and nonlinear singular value proposed by the first author recently, is obtained by numerical approach for the two-dimensional quasigeostrophic model in this paper. The difference between the linear and nonlinear fastest growing perturbations is demonstrated. Moreover, local nonlinear fastest growing perturbations are also found numerically. This is one of the essential differences between linear and nonlinear theories, since in former case there is no local fastest growing perturbation. The results show that the nonlinear local fastest growing perturbations play a more important role in the study of the first kind of predictability than the nonlinear global fastest growing perturbation.展开更多
基金supported by the National Natural Science Foundation of China(No.11471292)
文摘This paper deals with Hermite learning which aims at obtaining the target function from the samples of function values and the gradient values. Error analysis is conducted for these algorithms by means of approaches from convex analysis in the frame- work of multi-task vector learning and the improved learning rates are derived.
基金the National Key Basic Research Project, "Research on the FormationMechanism and Prediction Theory of Severe Synoptic Disasters in China" (Grand No. G1998040910), the National Natural Science Foundation of China (Grand Nos. 49775262 and 49823002) and t
文摘Nonlinear fastest growing perturbation, which is related to the nonlinear singular vector and nonlinear singular value proposed by the first author recently, is obtained by numerical approach for the two-dimensional quasigeostrophic model in this paper. The difference between the linear and nonlinear fastest growing perturbations is demonstrated. Moreover, local nonlinear fastest growing perturbations are also found numerically. This is one of the essential differences between linear and nonlinear theories, since in former case there is no local fastest growing perturbation. The results show that the nonlinear local fastest growing perturbations play a more important role in the study of the first kind of predictability than the nonlinear global fastest growing perturbation.
