Two-grid P 0 2
5
Citation
14
Reference
10
Related Paper
Citation Trend
Keywords:
Square-integrable function
When dealing with continuous numeric features, we usually adopt feature discretization. In this work, to find the best way to conduct feature discretization, we present some theoretical analysis, in which we focus on analyzing correctness and robustness of feature discretization. Then, we propose a novel discretization method called Local Linear Encoding (LLE). Experiments on two numeric datasets show that, LLE can outperform conventional discretization method with much fewer model parameters.
Robustness
Feature (linguistics)
Cite
Citations (5)
Euler method
Mode (computer interface)
Cite
Citations (2)
In this work the discretization of the Hénon-Heiles system obtained by applying the Monaco and Normand-Cyrot method is investigated. In order to obtain dynamically valid models, several approaches covering from the choice of terms in the difference equation originated from the discretization process to the increase of the discretization order are analyzed. As a conclusion it is shown that discretized models that preserve both the symmetry and the stability of their continuous counterpart can be obtained, even for large discretization steps.
Cite
Citations (2)
Cite
Citations (9)
Discretization of continuous attributes is an important link that the rough set theory applied to the practical issues,but there is a larger choice of numerical uncertainty of the general method of discretization.In this paper,the posture difference composed by numerical difference studys the difference problem,and the results applied to the process of discretization of continuous attributes,forming a new method of discretization of continuous attributes based on the numerical difference analysis,resolving the issue of its uncertain,and finally giving a examples to verify.
Cite
Citations (0)
In this paper we study a class of multilevel high order time discretization procedures for the finite difference weighted essential non-oscillatory (WENO) schemes to solve the one-dimensional and two-dimensional shallow water equations with source terms. Multilevel time discretization methods can make full use of computed information by WENO spatial discretization and save CPU cost by holding the former computational values. Extensive simulations are performed, which indicate that, the finite difference WENO schemes with multilevel time discretization can achieve higher accuracy, and are more cost effective than WENO scheme with Runge-Kutta time discretization, while still maintaining nonoscillatory properties.
Finite difference
Shallow water equations
Runge–Kutta methods
Cite
Citations (5)
Adjacency list
Cite
Citations (42)
Cite
Citations (0)
Cite
Citations (4)
1.1 MotivationWhy do mathematicians use Sobolev spaces instead of the simpler looking spaces of continuously differentiable functions?The most famous Sobolev space is H1(Ω), the set of all functions u which are square integrable, together with all their first derivatives, in Ω, an open subset of ℝn, the usual n-dimensional Euclidian space. The derivatives are to be understood in the sense of distributions. It is not even true that any function in H1(Ω) is continuous. For instance, the functionu(x,y)=|ln12(x2+y2)|1/3is in H1(Ω1), where Ω1 is the unit circle in the plane:Ω1={(x,y)∈ℝ2,x2+y2<1}.However, u is not continuous at (0, 0) and not even bounded. Such spaces are obviously not easy to handle.
Square-integrable function
Locally integrable function
Sobolev inequality
Cite
Citations (42)