Template-based smoothing functions for data smoothing in Geodesy

This paper is aimed at the derivation of a discrete data smoothing function for the discrete Dirichlet condition in a regular grid on the surface of a spheroid.The method employed here is the local L^2-seminorm minimization,through Euler-Lagrange method,for the Beltrami operator.The method results in a weighted average of the surrounding points in a te mplate based on the first order Taylor expansion of the unknown function under consideration.The coefficients of the weighted average are calculated and used to smooth the Geoid height data in Iran,derived from the EGM2008 geopotential model.

A NEW FORMULATION OF BERNSTEIN-BEZIER BASED SMOOTHNESS CONDITIONS FOR pp FUNCTIONS

In this note, we establish a new formulation of smoothness conditions for piecewise polynomial (: =pp) functions in terms of the B-net representation in the general n-dimensional setting. It plays an important role for 2-dimensional setting in the constructive proof of the fact that the spaces of polynomial splines with smoothness rand total degree k≥3r+2 over arbitrary triangulations achieve the optimal approximation order with the approximation constant depending only on k and the smallest angle of the partition in [5].

A Class of Smoothing Modulus-Based Iterative Method for Solving Implicit Complementarity Problems

In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point equation, then introduces a smoothing function to obtain its approximation solutions. The convergence analysis of the algorithm was given, and the efficiency of the algorithms was verified by numerical experiments.

Two-dimensional finite element mesh generation algorithm for electromagnetic field calculation

Two-dimensional finite element mesh generation algorithm for electromagnetic field calculation is proposed in this paper to improve the efficiency and accuracy of electromagnetic calculation. An image boundary extraction algorithm is developed to map the image on the geometric domain. Identification algorithm for the location of nodes in polygon area is proposed to determine the state of the node. To promote the average quality of the mesh and the efficiency of mesh generation, a novel force-based mesh smoothing algorithm is proposed. One test case and a typical electromagnetic calculation are used to testify the effectiveness and efficiency of the proposed algorithm. The results demonstrate that the proposed algorithm can produce a high-quality mesh with less iteration.

A Cell-Based Linear Smoothed Finite Element Method for Polygonal Topology Optimization

The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.

Smoothing Approximations for Some Piecewise Smooth Functions

In this paper,we study smoothing approximations for some piecewise smooth functions.We first present two approaches for one-dimensional case:a global approach is to construct smoothing approximations over the whole domain and a local approach is to construct smoothing approximations within appropriate neighborhoods of the nonsmooth points.We obtain some error estimate results for both approaches and discuss whether the smoothing approximations can inherit the convexity of the original functions.Furthermore,we extend the global approach to some multiple dimensional cases.

Solving Smooth Generalized Equations Using Modified Gauss-Type Proximal Point Method

Consider X and Y are two real or complex Banach spaces. We introduce and study a modified Gauss-type proximal point algorithm (in short modified G-PPA) for solving the generalized equations of the form 0 ∈h(x) + H(x), where h : X → Y is a smooth function on Ω ⊆X and H : X ⇉2Y is a set valued mapping with closed graph. When H is metrically regular and under some sufficient conditions, we analyze both semi-local and local convergence of the modified G-PPA. Moreover, the convergence results of the modified G-PPA are justified by presenting a numerical example.

Simulation of Oil-Water Flow in Shale Oil Reservoirs Based on Smooth Particle Hydrodynamics

A Smooth Particle Hydrodynamics(SPH)method is employed to simulate the two-phase flow of oil and water in a reservoir.It is shown that,in comparison to the classical finite difference approach,this method is more stable and effective at capturing the complex evolution of this category of two-phase flows.The influence of several smooth functions is explored and it is concluded that the Gaussian function is the best one.After 200 days,the block water cutoff for the Gaussian function is 0.3,whereas the other functions have a block water cutoff of 0.8.The effect of various injection ratios on real reservoir production is explored.When 14 and 8 m^(3)/day is employed,the water breakthrough time is 130 and 170 days,respectively,and the block produces 9246 m^(3) and 6338 m^(3) of oil cumulatively over 400 days.

某些周期函数类的N宽度

This paper considers the Kolmogorov width,the Gelfand width and the Linear width of the periodic smooth functions with boundary conditions in Orlicz space.Further,the relationships among these three types of width are obtained.

An Efficient Smooth Quantile Boost Algorithm for Binary Classification

In this paper, we propose a Smooth Quantile Boost Classification (SQBC) algorithm for binary classification problem. The SQBC algorithm directly uses a smooth function to approximate the “check function” of the quantile regression. Compared to other boost-based classification algorithms, the proposed algorithm is more accurate, flexible and robust to noisy predictors. Furthermore, the SQBC algorithm also can work well in high dimensional space. Extensive numerical experiments show that our proposed method has better performance on randomly simulations and real data.

Operations with Higher-Order Types of Asymptotic Variation: Filling Some Gaps

In this paper we exhibit some results concerning operations with higher-order types of asymptotic variation, results lacking in the general theory developed in previous papers, namely: 1) we show to what extent the standard elementary factorization of a regularly-varying function holds true for higher-order variation;2) we exhibit an important class of higher-order regularly-varying functions requiring no restrictions on the indexes when performing multiplication;3) we get non-obvious results on the types of higher-order variation for linear combinations. In addition, partial results are obtained concerning the type of higher-order variation of the inverse of a regularly-varying function whose index belongs to a set of “exceptional” values.

A High Order Method for Determining the Edges in the Gradient of a Function

Detection of edges in piecewise smooth functions is important in many applications.Higher order reconstruction algorithms in image processing and post processing of numerical solutions to partial differential equations require the identification of smooth domains,creating the need for algorithms that will accurately identify discontinuities in a given function as well as those in its gradient.This work expands the use of the polynomial annihilation edge detector,(Archibald,Gelb and Yoon,2005),to locate discontinuities in the gradient given irregularly sampled point values of a continuous function.The idea is to preprocess the given data by calculating the derivative,and then to use the polynomial annihilation edge detector to locate the jumps in the derivative.We compare our results to other recently developed methods.

Application of smoothing technique on twin support vector hypersphere

In order to improve the learning speed and reduce computational complexity of twin support vector hypersphere(TSVH),this paper presents a smoothed twin support vector hypersphere(STSVH)based on the smoothing technique.STSVH can generate two hyperspheres with each one covering as many samples as possible from the same class respectively.Additionally,STSVH only solves a pair of unconstraint differentiable quadratic programming problems(QPPs)rather than a pair of constraint dual QPPs which makes STSVH faster than the TSVH.By considering the differentiable characteristics of STSVH,a fast Newton-Armijo algorithm is used for solving STSVH.Numerical experiment results on normally distributed clustered datasets(NDC)as well as University of California Irvine(UCI)data sets indicate that the significant advantages of the proposed STSVH in terms of efficiency and generalization performance.

ESTIMATION AND UNCERTAINTY QUANTIFICATION FOR PIECEWISE SMOOTH SIGNAL RECOVERY

This paper presents an application of the sparse Bayesian learning(SBL)algorithm to linear inverse problems with a high order total variation(HOTV)sparsity prior.For the problem of sparse signal recovery,SBL often produces more accurate estimates than maximum a posteriori estimates,including those that useℓ1 regularization.Moreover,rather than a single signal estimate,SBL yields a full posterior density estimate which can be used for uncertainty quantification.However,SBL is only immediately applicable to problems having a direct sparsity prior,or to those that can be formed via synthesis.This paper demonstrates how a problem with an HOTV sparsity prior can be formulated via synthesis,and then utilizes SBL.This expands the class of problems available to Bayesian learning to include,e.g.,inverse problems dealing with the recovery of piecewise smooth functions or signals from data.Numerical examples are provided to demonstrate how this new technique is effectively employed.

A new technique of integral representations in C^(n)

A new technique of integral representations in Cn, which is different from the well-known Henkin technique, is given. By means of this new technique, a new integral formula for smooth functions and a new integral representation of solutions of the -equations on strictly pseudoconvex domains in Cn are obtained. These new formulas are simpler than the classical ones, especially the solutions of the -equations admit simple uniform estimates. Moreover, this new technique can be further applied to arbitrary bounded domains in Cn so that all corresponding formulas are simplified.