Based on the Crank-Nicolson and the weighted and shifted Grunwald operators,we present an implicit difference scheme for the Riesz space fractional reaction-dispersion equations and also analyze the stability and the ...Based on the Crank-Nicolson and the weighted and shifted Grunwald operators,we present an implicit difference scheme for the Riesz space fractional reaction-dispersion equations and also analyze the stability and the convergence of this implicit difference scheme.However,after estimating the condition number of the coefficient matrix of the discretized scheme,we find that this coefficient matrix is ill-conditioned when the spatial mesh-size is sufficiently small.To overcome this deficiency,we further develop an effective banded M-matrix splitting preconditioner for the coefficient matrix.Some properties of this preconditioner together with its preconditioning effect are discussed.Finally,Numerical examples are employed to test the robustness and the effectiveness of the proposed preconditioner.展开更多
Patch-level features are essential for achieving good performance in computer vision tasks. Besides well- known pre-defined patch-level descriptors such as scalein- variant feature transform （SIFT） and histogram of ...Patch-level features are essential for achieving good performance in computer vision tasks. Besides well- known pre-defined patch-level descriptors such as scalein- variant feature transform （SIFT） and histogram of oriented gradient （HOG）, the kernel descriptor （KD） method [1] of- fers a new way to ＂grow-up＂ features from a match-kernel defined over image patch pairs using kernel principal compo- nent analysis （KPCA） and yields impressive results. In this paper, we present efficient kernel descriptor （EKD） and efficient hierarchical kernel descriptor （EHKD）, which are built upon incomplete Cholesky decomposition. EKD au- tomatically selects a small number of pivot features for gener- ating patch-level features to achieve better computational effi- ciency. EHKD recursively applies EKD to form image-level features layer-by-layer. Perhaps due to parsimony, we find surprisingly that the EKD and EHKD approaches achieved competitive results on several public datasets compared with other state-of-the-art methods, at an improved efficiency over KD.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12161030)by the Hainan Provincial Natural Science Foundation of China(Grant No.121RC537).
文摘Based on the Crank-Nicolson and the weighted and shifted Grunwald operators,we present an implicit difference scheme for the Riesz space fractional reaction-dispersion equations and also analyze the stability and the convergence of this implicit difference scheme.However,after estimating the condition number of the coefficient matrix of the discretized scheme,we find that this coefficient matrix is ill-conditioned when the spatial mesh-size is sufficiently small.To overcome this deficiency,we further develop an effective banded M-matrix splitting preconditioner for the coefficient matrix.Some properties of this preconditioner together with its preconditioning effect are discussed.Finally,Numerical examples are employed to test the robustness and the effectiveness of the proposed preconditioner.
文摘Patch-level features are essential for achieving good performance in computer vision tasks. Besides well- known pre-defined patch-level descriptors such as scalein- variant feature transform （SIFT） and histogram of oriented gradient （HOG）, the kernel descriptor （KD） method [1] of- fers a new way to ＂grow-up＂ features from a match-kernel defined over image patch pairs using kernel principal compo- nent analysis （KPCA） and yields impressive results. In this paper, we present efficient kernel descriptor （EKD） and efficient hierarchical kernel descriptor （EHKD）, which are built upon incomplete Cholesky decomposition. EKD au- tomatically selects a small number of pivot features for gener- ating patch-level features to achieve better computational effi- ciency. EHKD recursively applies EKD to form image-level features layer-by-layer. Perhaps due to parsimony, we find surprisingly that the EKD and EHKD approaches achieved competitive results on several public datasets compared with other state-of-the-art methods, at an improved efficiency over KD.
