In the smoothed particle hydrodynamics (SPH) method, a meshless interpolation scheme is needed for the unknown function in order to discretize the governing equation.A particle approximation method has so far been use...In the smoothed particle hydrodynamics (SPH) method, a meshless interpolation scheme is needed for the unknown function in order to discretize the governing equation.A particle approximation method has so far been used for this purpose.Traditional particle interpolation (TPI) is simple and easy to do, but its low accuracy has become an obstacle to its wider application.This can be seen in the cases of particle disorder arrangements and derivative calculations.There are many different methods to improve accuracy, with the moving least square (MLS) method one of the most important meshless interpolation methods.Unfortunately, it requires complex matrix computing and so is quite time-consuming.The authors developed a simpler scheme, called higher-order particle interpolation (HPI).This scheme can get more accurate derivatives than the MLS method, and its function value and derivatives can be obtained simultaneously.Although this scheme was developed for the SPH method, it has been found useful for other meshless methods.展开更多
In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate ...In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate of higher accuracy of this new element for the Sobolev type equations.展开更多
For a Jordan domain D in the complex plane satisfying certain boundary conditions a function f B(D), we prove that the corresponding higher order Fejer interpolation polynomials based on Fejer points converge to f(z...For a Jordan domain D in the complex plane satisfying certain boundary conditions a function f B(D), we prove that the corresponding higher order Fejer interpolation polynomials based on Fejer points converge to f(z) uniformly on D. These extend some known results.展开更多
Let X<sub>n</sub>={x<sub>kn</sub>=cosθ<sub>kn</sub>: θ<sub>kn</sub>=（kπ）/（n+1）, 1≤k≤n}be the node system which consists ofroots of U<sub>n</sub> （x...Let X<sub>n</sub>={x<sub>kn</sub>=cosθ<sub>kn</sub>: θ<sub>kn</sub>=（kπ）/（n+1）, 1≤k≤n}be the node system which consists ofroots of U<sub>n</sub> （x） =（sin（n+1）θ）/（sinθ）（x=cosθ θ∈[0,π]）, the second kind Chebyshevpolynomical. All the symbols below have the same meaning as Ref. [1]if notspecifically defined. We shall consider a kind of new interpolating problem in thisnote. For any non-negative integer q and f∈C[-1, 1], it is well known that thepolynomial Q<sub>nq</sub>（f）∈П<sub>N</sub> （N=2（q+1） （n+1） -1） satisfying the following conditions isuniquely determined:Q<sub>nq</sub>(f, x<sub>kn</sub>) =f(x<sub>kn</sub>), 1≤k≤n; Q<sub>nq</sub>（f,±1）=f（±1）,Q<sub>nq</sub><sup>j</sup>(f,x<sub>kn</sub>)=c<sub>jkn</sub>, 1≤k≤n,1≤j≤2q+1,Q<sub>nq</sub><sup>j</sup>（f,1）=d<sub>jn</sub>, Q<sub>nq</sub><sup>j</sup>（f,-1）=g<sub>jn</sub>, 1≤j≤q,where c<sub>jkn</sub>,d<sub>jn</sub>, g<sub>jn</sub>are any given real numbers. Q<sub>nq</sub>（f）is called the higher orderquasi Hermite-Fejer interpolation of f.We展开更多
对传感器阵列信号波达方向(DOA,direction of arrival)估计算法研究多集中在均匀线阵、圆阵等规则阵型阵列,但在水下传感网络等应用环境中阵元分布具有一定随机性,阵列呈现不规则特点.论文利用虚拟阵元思想,通过对不规则阵列的虚拟内插...对传感器阵列信号波达方向(DOA,direction of arrival)估计算法研究多集中在均匀线阵、圆阵等规则阵型阵列,但在水下传感网络等应用环境中阵元分布具有一定随机性,阵列呈现不规则特点.论文利用虚拟阵元思想,通过对不规则阵列的虚拟内插,在逻辑上构建多个具有相同配置参数的子阵列;对多个结构相同的子阵,利用空间平滑技术进行相关目标方位估计;为消除内插引入的非高斯有色噪声影响,引入信号高阶累积量,用累积量矩阵代替协方差矩阵,保证算法精确高效.通过计算机仿真,首先对比了不同信噪比和快拍数条件下提出的算法与传统算法性能,其次研究了构建子阵时角度间隔的取值对估计结果的影响,最后定量分析了特定信噪比和快拍数下新算法DOA估计的平均偏差和标准差,结果显示,新算法能有效提高估计精度.展开更多
红边(REP)是绿色植物叶子光谱曲线在680nm～740nm之间变化率最快的点,也是一阶导数光谱在该区间内的拐点。本文总结了红边参数的种类,红边在植物种类的识别、植物时相的识别、植物生物参数估测和植物生长状况监测等方面的应用,并介绍了...红边(REP)是绿色植物叶子光谱曲线在680nm～740nm之间变化率最快的点,也是一阶导数光谱在该区间内的拐点。本文总结了红边参数的种类,红边在植物种类的识别、植物时相的识别、植物生物参数估测和植物生长状况监测等方面的应用,并介绍了红边参数其适用范围和使用方法等,阐述了红边在植被研究中的重要性,分析了植被红边技术的发展方向和应用前景;同时总结了线性内插模型、反高斯模型、拉格朗日模型、多项式模型和有理函数新模型等五种红边定量分析方法及应用,以及它们的适用范围等,并介绍了G.V.G.BARANOS-KI and J.G.ROKNE采用有理函数新模型分析过程以确定红边位置的"新"方法。展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10572041,50779008Doctoral Fund of Ministry of Education of China under Grant No.20060217009
文摘In the smoothed particle hydrodynamics (SPH) method, a meshless interpolation scheme is needed for the unknown function in order to discretize the governing equation.A particle approximation method has so far been used for this purpose.Traditional particle interpolation (TPI) is simple and easy to do, but its low accuracy has become an obstacle to its wider application.This can be seen in the cases of particle disorder arrangements and derivative calculations.There are many different methods to improve accuracy, with the moving least square (MLS) method one of the most important meshless interpolation methods.Unfortunately, it requires complex matrix computing and so is quite time-consuming.The authors developed a simpler scheme, called higher-order particle interpolation (HPI).This scheme can get more accurate derivatives than the MLS method, and its function value and derivatives can be obtained simultaneously.Although this scheme was developed for the SPH method, it has been found useful for other meshless methods.
基金the National Natural Science Foundation of China(10671184)
文摘In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate of higher accuracy of this new element for the Sobolev type equations.
文摘For a Jordan domain D in the complex plane satisfying certain boundary conditions a function f B(D), we prove that the corresponding higher order Fejer interpolation polynomials based on Fejer points converge to f(z) uniformly on D. These extend some known results.
文摘Let X<sub>n</sub>={x<sub>kn</sub>=cosθ<sub>kn</sub>: θ<sub>kn</sub>=（kπ）/（n+1）, 1≤k≤n}be the node system which consists ofroots of U<sub>n</sub> （x） =（sin（n+1）θ）/（sinθ）（x=cosθ θ∈[0,π]）, the second kind Chebyshevpolynomical. All the symbols below have the same meaning as Ref. [1]if notspecifically defined. We shall consider a kind of new interpolating problem in thisnote. For any non-negative integer q and f∈C[-1, 1], it is well known that thepolynomial Q<sub>nq</sub>（f）∈П<sub>N</sub> （N=2（q+1） （n+1） -1） satisfying the following conditions isuniquely determined:Q<sub>nq</sub>(f, x<sub>kn</sub>) =f(x<sub>kn</sub>), 1≤k≤n; Q<sub>nq</sub>（f,±1）=f（±1）,Q<sub>nq</sub><sup>j</sup>(f,x<sub>kn</sub>)=c<sub>jkn</sub>, 1≤k≤n,1≤j≤2q+1,Q<sub>nq</sub><sup>j</sup>（f,1）=d<sub>jn</sub>, Q<sub>nq</sub><sup>j</sup>（f,-1）=g<sub>jn</sub>, 1≤j≤q,where c<sub>jkn</sub>,d<sub>jn</sub>, g<sub>jn</sub>are any given real numbers. Q<sub>nq</sub>（f）is called the higher orderquasi Hermite-Fejer interpolation of f.We
文摘对传感器阵列信号波达方向(DOA,direction of arrival)估计算法研究多集中在均匀线阵、圆阵等规则阵型阵列,但在水下传感网络等应用环境中阵元分布具有一定随机性,阵列呈现不规则特点.论文利用虚拟阵元思想,通过对不规则阵列的虚拟内插,在逻辑上构建多个具有相同配置参数的子阵列;对多个结构相同的子阵,利用空间平滑技术进行相关目标方位估计;为消除内插引入的非高斯有色噪声影响,引入信号高阶累积量,用累积量矩阵代替协方差矩阵,保证算法精确高效.通过计算机仿真,首先对比了不同信噪比和快拍数条件下提出的算法与传统算法性能,其次研究了构建子阵时角度间隔的取值对估计结果的影响,最后定量分析了特定信噪比和快拍数下新算法DOA估计的平均偏差和标准差,结果显示,新算法能有效提高估计精度.
文摘红边(REP)是绿色植物叶子光谱曲线在680nm～740nm之间变化率最快的点,也是一阶导数光谱在该区间内的拐点。本文总结了红边参数的种类,红边在植物种类的识别、植物时相的识别、植物生物参数估测和植物生长状况监测等方面的应用,并介绍了红边参数其适用范围和使用方法等,阐述了红边在植被研究中的重要性,分析了植被红边技术的发展方向和应用前景;同时总结了线性内插模型、反高斯模型、拉格朗日模型、多项式模型和有理函数新模型等五种红边定量分析方法及应用,以及它们的适用范围等,并介绍了G.V.G.BARANOS-KI and J.G.ROKNE采用有理函数新模型分析过程以确定红边位置的"新"方法。
