迭代方程与离散叙率Walsh函数

在J.L.Shanks的基础上,给出了产生离散叙率Walsh函数的迭代方程,由迭代 方程推出了离散Walsh 函数的表达式和Walsh变换的速算 法(FWWT).     

C编号Walsh函数及Manz算法

沃尔什编号Walsh函数是Walsh在1923年给出的;1931年,Paley定义了佩利编号Walsh函数;哈德玛编号Walsh函数是根据Hadamard 1893年的工作,由专用     

关于Chrestenson变换的功率谱

一、引言离散 Walsh-Hadamard 变换与离散 Fourier 变换一样,是信号处理的重要工具之一.1955年 N.E.Chrestenson 和 R.G.Selfridge 将 Walsh 函数推广为 p 进情形.对这种广义 Walsh 函数所对应的离散情形的研究亦已获得不少进展,特别是由于它与线性 p     

离散系统分析和参数估计的DPOFS方法

本文借助于DPOFS(离散正交脉冲函数)对离散线性系统和离散双线性系统的分析和参数估计提出了新的方法,这种方法利用:DPOFS的运算矩阵把差分方程转变为代数方程,并由于DPOFS比离散Walsh级数等离散级数在计算方面更加方便和直观,从而使计算大大简化,本文给出了具体实例,分析结果说明了此法的有效性。     

分数阶Burgers方程的有限元计算(英文)

建立了一维和二维分数阶Burgers方程的有限元格式.时间分数阶导数使用L1方法离散,空间方向使用有限元方法离散.通过选择合适的基函数,将离散后的方程转化成一个非线性代数方程组,并应用牛顿迭代方法求解.数值实验显示出了方法的有效性.     

解离散HJB方程的一个单调迭代法

本文对离散HJB方程提出一类新的迭代法,产生的迭代解单调收敛于HJB方程的解.此法的优点是简单易行.     

斜Haar类变换的演化生成与快速算法

1.引 言 Haar函数和Walsh函数是两类密切相关且十分重要的完备正交函数系,它们不仅在(离散)正交变换及其快速算法设计中起着重要的作用,而且在小波分析中占有重要地位:它们分别对应于Haar小波和Haar小波包.另外,它们还是遗传算法和密码学等涉及布尔函数或离散函数的学科之重要的理论分析工具.     

抛物方程时间周期问题的有限元多格子动力学迭代

本文我们研究线性周期抛物方程的有限元多格子动力学迭代.多格子动力学迭代又称多重网格波形松弛,它是在函数空间中的一种迭代过程.对于由加速技术得到的多格子动力学迭代算子,我们通过计算周期函数的Fourier系数给出了新的谱表达式.从这些有用的表达式出发,我们推导了时间连续和离散格式的迭代收敛条件.数值实验进一步验证了本文的理论结果.     

布尔函数的迹Walsh谱

布尔函数线性Walsh谱和高阶Walsh谱的研究对构造能够抵抗线性逼近攻击和二次或较高次逼近攻击的密码函数发挥了重要作用.为了抵抗采样攻击,提出了布尔函数迹Walsh谱和迹Walsh循环谱概念,并给出该Walsh谱的一些简单性质.利用这一谱值的分布特性,可以很好地分析布尔函数的迹函数逼近问题,对序列密码采样攻击研究具有重要意义.     

Walsh函数的一种新定义及快速算法设计

传统的Walsh函数是以Rademacher函数为基函数生成 .本文运用对称复制的观点 ,定义了一种新函数 G函数 ,并以G函数为基础 ,定义了四种序的Walsh函数 ,同时 ,运用序码分析方法 ,实现了两种序Walsh变换的快速算法设计 .     

Frequency domain Walsh functions and sequences: An introduction

In this letter, a new set of orthogonal band-limited basis functions is introduced. This set of basis functions is derived from the inverse Fourier transform of the frequency domain Walsh functions. The Fourier transforms of the Walsh functions were calculated by Siemens and Kitai in 1973 but they have been overlooked in the literature. Some of the properties of these functions are studied in this paper. Moreover, the orthogonal discrete version of these functions is obtained by truncation, sampling and orthogonalization utilizing the orthogonal Procrustes problem.     

Multisymplectic variational integrators for PDEs of geometrically exact beam dynamics using algorithmic differentiation

For the simulation of geometrically exact beam dynamics [4], a multisymplectic Lie-group variational integrator [3] is derived. Based on the implementation of the discrete Lagrangian, algorithmic differentiation is used in the computation of both, the discrete Euler-Lagrange equations, and the Jacobi matrix needed for the Newton-Raphson iteration. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于Lie群的刚体动力学建模及数值计算方法研究

基于Lie群和Lie代数之间的指数映射等价关系,推导了基于Lie群的自由刚体连续动力学方程.结合离散变分原理,推导了其Lie群离散变分积分子.通过证明可知连续和离散动力学系统都具有动量守恒性.对连续动力学方程进行同维化处理,使其变为常规非线性方程组的形式,利用Runge-Kutta法进行求解;基于Runge-Kutta基本理论,推导了直接用于Lie群的Runge-Kutta法,从而使Runge-Kutta法可用于求解变维非线性方程组;通过Lie代数变换,利用Kelly变换和Newton迭代对Lie群离散变分积分子进行求解.仿真对比结果表明,3种算法下的计算结果高度吻合,且能高精度地保持系统的结构守恒和动量守恒性.     

Spectral Decomposition of Cyclic Operators in Discrete Harmonic Analysis

For the operators of the discrete Fourier transform, the discrete Vilenkin–Christenson transform, and all linear transpositions of the discrete Walsh transform, we obtain their spectral decompositions and calculate the dimensions of eigenspaces. For complex operators, namely, the discrete Fourier transform and the Vilenkin–Christenson transform, we obtain real projectors on eigenspaces. For the discrete Walsh transform, we consider in detail the Paley and Walsh orderings and a new ordering in which the matrices of operators are symmetric. For operators of linear transpositions of the discrete Walsh transforms with nonsymmetric matrices, we obtain a spectral decomposition with complex projectors on eigenspaces. We also present the Parseval frame for eigenspaces of the discrete Walsh transform.     

一类线性约束矩阵不等式及其最小二乘问题

本文主要考虑一类线性矩阵不等式及其最小二乘问题,它等价于相应的矩阵不等式最小非负偏差问题.之前相关文献提出了求解该类最小非负偏差问题的迭代方法,但该方法在每步迭代过程中需要精确求解一个约束最小二乘子问题,因此对规模较大的问题,整个迭代过程需要耗费巨大的计算量.为了提高计算效率,本文在现有算法的基础上,提出了一类修正迭代方法.该方法在每步迭代过程中利用有限步的矩阵型LSQR方法求解一个低维矩阵Krylov子空间上的约束最小二乘子问题,降低了整个迭代所需的计算量.进一步运用投影定理以及相关的矩阵分析方法证明了该修正算法的收敛性,最后通过数值例子验证了本文的理论结果以及算法的有效性.     

On the boundedness of the L1-norm of Walsh–Fejér kernels

In this paper we establish an iteration for the $L^1$-norm of Walsh–Fejér kernels with the assumption that the Walsh functions are ordered in Paley's sense. We use this iteration to prove some properties of this sequence, including that its supremum is exactly equal to $\frac{17}{15}$.     

Solving time‐periodic fractional diffusion equations via diagonalization technique and multigrid

This paper addresses numerical computation of time‐periodic diffusion equations with fractional Laplacian. Time‐periodic differential equations present fundamental challenges for numerical computation because we have to consider all the discrete solutions once in all instead of one by one. An idea based on the diagonalization technique is proposed, which yields a direct parallel‐in‐time computation for all the discrete solutions. The major computation cost is therefore reduced to solve a series of independent linear algebraic systems with complex coefficients, for which we apply a multigrid method using the damped Richardson iteration as the smoother. Such a linear solver possesses mesh‐independent convergence factor, and we make an optimization for the damping parameter to minimize such a constant convergence factor. Numerical results are provided to support our theoretical analysis.     

Policy iteration for robust nonstationary Markov decision processes

Policy iteration is a well-studied algorithm for solving stationary Markov decision processes (MDPs). It has also been extended to robust stationary MDPs. For robust nonstationary MDPs, however, an “as is” execution of this algorithm is not possible because it would call for an infinite amount of computation in each iteration. We therefore present a policy iteration algorithm for robust nonstationary MDPs, which performs finitely implementable approximate variants of policy evaluation and policy improvement in each iteration. We prove that the sequence of cost-to-go functions produced by this algorithm monotonically converges pointwise to the optimal cost-to-go function; the policies generated converge subsequentially to an optimal policy.