A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in th...A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in the L2 norm and nodal supercnnvergence. These results generalize those obtained earlier by Hulme for continuous piecevjise polynomials and by Delfour-Dubeau for discontinuous pieceuiise polynomials. A duality relationship for the two types of approximations is also given.展开更多
The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear probl...The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.展开更多
Although important progresses have been already made in face detection,many false faces can be found in detection results and false detection rate is influenced by some factors,such as rotation and tilt of human face,...Although important progresses have been already made in face detection,many false faces can be found in detection results and false detection rate is influenced by some factors,such as rotation and tilt of human face,complicated background,illumination,scale,cloak and hairstyle.This paper proposes a new method called DP-Adaboost algorithm to detect multi-angle human face and improve the correct detection rate.An improved Adaboost algorithm with the fusion of frontal face classifier and a profile face classifier is used to detect the multi-angle face.An improved horizontal differential projection algorithm is put forward to remove those non-face images among the preliminary detection results from the improved Adaboost algorithm.Experiment results show that compared with the classical Adaboost algorithm with a frontal face classifier,the textual DP-Adaboost algorithm can reduce false rate significantly and improve hit rate in multi-angle face detection.展开更多
基金This research has been supported in part by the Natural Sciences and Engineering Research Council of Canada(Grant OGPIN-336)and by the"Ministere de l'Education du Quebec"(FCAR Grant-ER-0725)
文摘A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in the L2 norm and nodal supercnnvergence. These results generalize those obtained earlier by Hulme for continuous piecevjise polynomials and by Delfour-Dubeau for discontinuous pieceuiise polynomials. A duality relationship for the two types of approximations is also given.
基金supported by the National Natural Science Foundation of China(Nos.51378293,51078199,50678093,and 50278046)the Program for Changjiang Scholars and the Innovative Research Team in University of China(No.IRT00736)
文摘The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.
文摘Although important progresses have been already made in face detection,many false faces can be found in detection results and false detection rate is influenced by some factors,such as rotation and tilt of human face,complicated background,illumination,scale,cloak and hairstyle.This paper proposes a new method called DP-Adaboost algorithm to detect multi-angle human face and improve the correct detection rate.An improved Adaboost algorithm with the fusion of frontal face classifier and a profile face classifier is used to detect the multi-angle face.An improved horizontal differential projection algorithm is put forward to remove those non-face images among the preliminary detection results from the improved Adaboost algorithm.Experiment results show that compared with the classical Adaboost algorithm with a frontal face classifier,the textual DP-Adaboost algorithm can reduce false rate significantly and improve hit rate in multi-angle face detection.
