两种改进Lagrange插值格式的对比分析

本文基于Lagrange插值多项式,给出了两种改进的Lagrange插值格式：Aitken插值和重心Lagrange插值。从算法的复杂性及数值稳定性两个方面进行了比较分析,结果表明重心形式的Lagrange插值是最优的。文末给出数值试验表明算法的有效性。     

Static and free vibration analyses of functionally graded porous variable-thickness plates using an edge-based smoothed finite element method

The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous (FGP) variable-thickness plates by using an edge-based smoothed finite element method (ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element (MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index (k) and maximum porosity distributions (Ω) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.     

一种快速高精度的射表数据处理方法

介绍一种基于多结点样条函数的射表数据处理新方法。与弹道方程法和多项式函数逼近法的比较结果表明,本方法兼有快速、高精度和实现简便等优点。     

三角形网格上的C1有理插值

本文描述了一种用线性算子的组合插值新方法。较之已往方法,插值函数结构简单,易于计算。并且估计了插值函数的误差,误差阶是O(h~4),比[4]中的误差阶高2.     

点数任意时的快速插值算法

本文建立了运算量级为O(nlog_2m) 的多项式快速除法(其中,m,n分别为除式与被除式的多项式次数),把点数n+1为2的幂次的多项式快速插值推广到n+1为任意数情形,提出了运算量级为O (n log_2~2n) 的快速插值算法。     

一个 C1 单调保形插值三次样条的构造

本文利用三次Bernstein多项式构造了一种C~1单调保形插值三次样条函数。该方法除计算简单外,还能应用于外形设计中且能灵活地调节外形曲线。     

海上机动目标的运动预测模型及精度分析

分析了海上机动目标的运动特性,针对海上机动目标在某些时间段运动具有一定的规律性,用插值外推法建立了预测其运动的数学模型。并对此模型的精度进行了分析,最后给出了实例。仿真结果表明,本模型能适用于海上机动目标不同的机动方式,算法快捷,具有较强的军事应用价值,模型的计算精度完全满足某新型号导弹的作战要求。     

一种保持图像细节的形态学滤波器

提出了一种保持图像细节的形态学滤波器 .和经典形态学滤波器相比较 ,新的形态学滤波器在其主要算子中使用了结构元素的轮廓 .用测试图和加噪图进行实验 ,表明此滤波器具有良好的保护图像细节和滤噪的性能     

Convolutions and generalization of logconcavity: Implications and applications

Additive convolution of unimodal and α‐unimodal random variables are known as an old classic problem which has attracted the attention of many authors in theory and applied fields. Another type of convolution, called multiplicative convolution, is rather younger. In this article, we first focus on this newer concept and obtain several useful results in which the most important ones is that if is logconcave then so are and for some suitable increasing functions ?. This result contains and as two more important special cases. Furthermore, one table including more applied distributions comparing logconcavity of f(x) and and two comprehensive implications charts are provided. Then, these fundamental results are applied to aging properties, existence of moments and several kinds of ordered random variables. Multiplicative strong unimodality in the discrete case is also introduced and its properties are investigated. In the second part of the article, some refinements are made for additive convolutions. A remaining open problem is completed and a conjecture concerning convolution of discrete α‐unimodal distributions is settled. Then, we shall show that an existing result regarding convolution of symmetric discrete unimodal distributions is not correct and an easy alternative proof is presented. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 109–123, 2016     

利用实际飞行数据插值的INS/GNSS组合导航仿真轨迹发生器

针对INS/GNSS组合导航仿真中捷联惯导系统陀螺、加速度计信号高精度模拟问题,提出基于实际飞行数据插值的动态轨迹解析生成仿真算法。对转换到地心惯性坐标系中的载体姿态、位置和重力场数据进行关于时间的样条函数插值,得到载体坐标系下陀螺角速率、角增量以及加速度计比力积分增量的高精度分段解析表达式。使生成的陀螺、加速度计信号符合载体运动学和动力学特性,反映杆臂效应影响,同时与经事后处理的实测GNSS伪距、伪距率等数据特征保持一致。提出四元数约束插值算法,其可满足四元数解析插值时范数为1的约束限制条件。基于某实际无人机飞行数据,验证了所提算法的有效性,其完全满足组合导航动态仿真精度要求。该算法也适用于其他高精度高动态导航系统和刚体运动控制仿真中的角运动、线运动传感器信号模拟。