Unconditionally stable C1-cubic spline collocation method for solving parabolic equations

This article aims to present a new approach based on C¹-cubic splines introduced by Sallam and Naim Anwar [Sallam, S. and Naim Anwar, M. (2000). Stabilized cubic C¹-spline collocation method for solving first-order ordinary initial value problems, Int. J. Comput. Math., 74, 87–96.], which is A-stable, for the time integration of parabolic equations (diffusion or heat equation). The introduced method is an example of the so-called method of lines (the solution is thought to consist of space discretization and time integration), which is an extension of the 1/3-Simpson's finite-difference scheme. Our main objective is to prove the unconditional stability of the proposed method as well as to show that the method is convergent and is of order O (h ²)?+?O (k ⁴) i.e. it is a fourth-order in time and second-order in space. Computational results also show that the method is relevant for long time interval problems.     

Numerical integration of partial differential equations using cubic splines

This paper presents techniques for the numerical solution of partial differential equations using cubic spline collocation.

The main spline relations are presented and incorporated into solution procedures for partial differential equations. The computational algorithm in every case is a tridiagonal matrix system amenable to efficient inversion methods. Truncation errors and stability are briefly discussed. Finally, some examples of their application to parabolic and hyperbolic systems with mixed boundary conditions are presented.

The results obtained are encouraging and justify further research in this field.     

Geoadditive expectile regression

Quantile regression has emerged as one of the standard tools for regression analysis that enables a proper assessment of the complete conditional distribution of responses even in the presence of heteroscedastic errors. Quantile regression estimates are obtained by minimising an asymmetrically weighted sum of absolute deviations from the regression line, a decision theoretic formulation of the estimation problem that avoids a full specification of the error term distribution. Recent advances in mean regression have concentrated on making the regression structure more flexible by including nonlinear effects of continuous covariates, random effects or spatial effects. These extensions often rely on penalised least squares or penalised likelihood estimation with quadratic penalties and may therefore be difficult to combine with the linear programming approaches often considered in quantile regression. As a consequence, geoadditive expectile regression based on minimising an asymmetrically weighted sum of squared residuals is introduced. Different estimation procedures are presented including least asymmetrically weighted squares, boosting and restricted expectile regression. The properties of these procedures are investigated in a simulation study and an analysis on rental fees in Munich is provided where the geoadditive specification allows for an analysis of nonlinear effects of the size of flats or the year of construction and the spatial distribution of rents simultaneously.     

一种改进的群体智能寻路算法

以游戏中群体智能角色的路径搜索为研究背景,提出一种改进的群体智能寻路算法。该方法把游戏寻路过程划分成三个阶段:第一阶段为预处理阶段,针对特定的目标点,采取逆向路径搜索策略,建立最优解路径表。第二阶段,针对动态障碍物的避让,运用实时A*算法生成局部动态路径,并与初始路径进行拼接。第三阶段,对找到的路径进行关键点优化和Catmull-Rom样条平滑处理。实验结果表明该方法在游戏开发中的实用价值。     

Weighted thin-plate spline image denoising

This note aims to present new denoising method based on thin-plate splines (TPS). The proposed approach is based on the general TPS denoising Berman [2], however, its unfavorable smoothing of edges and details is suppressed by introduction of a weighting approach applied locally. The performance of the method is shown and compared to the original TPS denoising.     

Rapid and Accurate Contact Determination between Spline Models using ShellTrees

In this paper, we present an efficient algorithm for contact determination between spline models. We make use of a new hierarchy, called ShellTree , that comprises of spherical shells and oriented bounding boxes. Each spherical shell corresponds to a portion of the volume between two concentric spheres. Given large spline models, our algorithm decomposes each surface into Bézier patches as part of pre-processing. At runtime it dynamically computes a tight fitting axis-aligned bounding box across each Bézier patch and efficiently checks all such boxes for overlap. Using off-line and on-line techniques for tree construction, our algorithm computes ShellTrees for Bézier patches and performs fast overlap tests between them to detect collisions. The overall approach can trade off runtime performance for reduced memory requirements. We have implemented the algorithm and tested it on large models, each composed of hundred of patches. Its performance varies with the configurations of the objects. For many complex models composed of hundreds of patches, it can accurately compute the contacts in a few milliseconds.     

Using regression splines to assess the impact of information technology investments on productivity in the health care industry

Abstract. This paper explores the impact of information technology (IT) investments on productivity using a new technique, multivariate adaptive regression splines (MARS). We believe that it provides additional insights on the nature of the impact of IT investments on productivity. The results from our study are compared with findings from a previous study that has also used the same data set. While the results of a previous study indicate that IT investments have a positive but uniform impact on productivity, our study suggests that the impact of IT on productivity is not uniform but is contingent on other complementary factors. Our findings describe that the complementary relationship exists between IT and non‐IT related investments. Thus, improved organizational productivity cannot be expected from investment in IT alone but only together with non‐IT investments. Our findings also point out that further investment may not necessarily bring on higher organizational productivity.     

Hierarchical B-splines on regular triangular partitions

Multivariate splines have a wide range of applications in function approximation, finite element analysis and geometric modeling. They have been extensively studied in the last several decades, and specially the theory on bivariate B-splines over regular triangular partition is well developed. However, the above mentioned splines do not have local refinement property – a property that is very important in adaptive function approximation and level of detailed representation of geometric models. In this paper, we introduce the concept of hierarchial bivariate splines over regular triangular partitions and construct basis functions of such spline space that satisfy some nice properties. We provide some examples of hierarchical splines over triangular partitions in surface fitting and in solving numerical PDEs, and the results turn out to be promising.     

基于NURBS算法的工业机器人轨迹规划研究

轨迹规划是工业机器人研究领域的重要内容之一。为解决使用直线与圆弧逼近不规则曲线方法带来较大误差的问题,提出使用NURBS拟合自由曲线,并使用S形速度曲线来控制机器人末端的运动速度和加速度,使各个插补点的位置、速度和加速度能够连续,将之反推到关节空间可以得到各个关节的角度、角速度和角加速度。最后以IRB2600工业机器人为仿真本体,通过MATLAB仿真证明:NURBS和S形速度曲线相结合的方法可以得到在关节空间连续、平稳的运行轨迹、速度曲线、加速度曲线,减弱了因各关节角度、角速度、角加速度突变带来的冲击影响,优化了机器人运行轨迹。     

一种混合样条插值

本文构造了一种混合样条函数,它是用一次多项式函数及指数函数的结合来表示的。文章给出了这种混合样条的一般表达式,并证明插值问题解的存在性定理和误差估计定理,由此说明这种样条函数具有良好的逼近度和物理背景。