一种基于图像块的Legendre矩高精度快速算法

针对图像的Legendre正交矩计算量大和矩值求解过程中存在离散近似误差等问题,提出一种新的高精度快速计算图像Legendre矩方法.文中首先提出一种最大块优先分块策略,然后在此基础上,根据图像像素灰度值的取值特征将图像进行分块表示,以每个图像块为单位计算图像的Legendre矩.实验结果表明,与现有的快速算法相比,文中方法在保证矩值高精确的前提下,有效地减少了算术运算的次数,降低了计算复杂度,具有较快的计算速度.     

WSN中基于多项式的安全密钥建立方案

针对分层WSN节点的更新,使用二元对称多项式,提出一种安全的建立通信双方会话密钥方案。该方案可保证传输消息的秘密性和完整性,能有效地抵御攻击者对消息的非法篡改、替换和重放。此外,该方案支持通信双方更新会话密钥和增加对节点身份的认证,防止非法节点的欺骗攻击。通过分析可知,该方案和现有方案相比,具有更高的安全性,以及成本和效率的合理性。     

Saturation in multivariate simultaneous approximation

In this paper we present a new result on the saturation of sequences of linear operators in a multivariate and simultaneous setting. Specifically, a small o saturation result is obtained for the partial derivatives of the classical Bernstein bivariate operators on the unit simplex. Solutions of boundary value problems for certain partial differential equations of elliptic type play an important role.     

Sparse polynomial division using a heap

In 1974, Johnson showed how to multiply and divide sparse polynomials using a binary heap. This paper introduces a new algorithm that uses a heap to divide with the same complexity as multiplication. It is a fraction-free method that also reduces the number of integer operations for divisions of polynomials with integer coefficients over the rationals. Heap-based algorithms use very little memory and do not generate garbage. They can run in the CPU cache and achieve high performance. We compare our C implementation of sparse polynomial multiplication and division with integer coefficients to the routines of the Magma, Maple, Pari, Singular and Trip computer algebra systems.     

Model order reduction methods for coupled systems in the time domain using Laguerre polynomials

In this paper, based on Laguerre polynomials, we present new methods for model reduction of coupled systems in the time domain. By appropriately selected projection matrices, a reduced order system is produced to retain the topology structure of the original system. Meanwhile, it preserves a desired number of Laguerre coefficients of the system’s output, thereby providing good approximation accuracy. We also study the two-sided projection method in the time domain, as well as the stability of reduced order systems. Two numerical examples are used to illustrate the efficiency of the proposed methods.     

Characterizing the measures on the unit circle with exact quadrature formulas in the space of polynomials

In the present paper we characterize the measures on the unit circle for which there exists a quadrature formula with a fixed number of nodes and weights and such that it exactly integrates all the polynomials with complex coefficients. As an application we obtain quadrature rules for polynomial modifications of the Bernstein measures on [−1,1], having a fixed number of nodes and quadrature coefficients and such that they exactly integrate all the polynomials with real coefficients.     

Model order reduction of MIMO bilinear systems by multi-order Arnoldi method

In this paper, we present a time domain model order reduction method for multi-input multi-output (MIMO) bilinear systems by general orthogonal polynomials. The proposed method is based on a multi-order Arnoldi algorithm applied to construct the projection matrix. The resulting reduced model can match a desired number of expansion coefficient terms of the original system. The approximate error estimate of the reduced model is given. And we also briefly discuss the stability preservation of the reduced model in some cases. Additionally, in combination with Krylov subspace methods, we propose a two-sided projection method to generate reduced models which capture properties of the original system in the time and frequency domain simultaneously. The effectiveness of the proposed methods is demonstrated by two numerical examples.     

基于修正变分法开孔板和加强板结构的自由振动分析

为研究船舶开孔板和加强板结构的振动特性,用1阶剪切变形板理论描述各向同性板的位移场,并采用修正变分原理和区域分解方法建立板的离散动力学模型.每一块子域板的位移和转角分量通过第一类切比雪夫正交多项式展开.针对加强板模型,将该方法获得的结果与已经发表的文献和有限元商用软件计算结果进行对比,验证该方法的收敛性和正确性.基于修正变分法探讨多种开孔和加强板模型的自由振动特性,充分说明该数理模型和半解析方法是一种适合处理复杂板结构问题的数值工具.     

一种深度图像中的表面曲率估计算法

曲率估计在深度图像分析中占有重要地位,传统的有限差分或局部拟合方法未考虑到表面上可能出现的不连续性,因而会不可避免地出现错误,为了得到有效可靠的曲率估计,本文提出了基于自适应局部表面拟合和鲁棒最大似然的估计的曲率估计算法,首先,提出曲面是分片光滑的假设,表面曲率需从该像素所属的光滑曲面片来估计,其次,定义了能量函数来度量拟合窗的平滑度,在局部表面拟合时,依据最小化能量函数的原则来自适应移动拟合窗的中心,以使拟合窗达到最“光滑”,最后,采用鲁棒最大似然估计以消除仍然存在的“局外点”的影响,理论分析和实验结果证明估计算法是稳健,可靠,有效的且计算复杂度小。     

Sparse shape functions for tetrahedral <Emphasis Type="Italic">p</Emphasis>-FEM using integrated Jacobi polynomials

Summary In this paper, we investigate the discretization of an elliptic boundary value problem in 3D by means of the hp-version of the finite element method using a mesh of tetrahedrons. We present several bases based on integrated Jacobi polynomials in which the element stiffness matrix has nonzero entries, where p denotes the polynomial degree. The proof of the sparsity requires the assistance of computer algebra software. Several numerical experiments show the efficiency of the proposed bases for higher polynomial degrees p.