递归方程求解方法综述

随着计算机科学的逐步发展,各种各样的算法相继出现,我们需要对算法进行分析,以选择性能更好的解决方案。算法分析中计算复杂度常用递归方程来表达,因此递归方程的求解有助于分析算法设计的好坏。阐述了常用的3种求解递归方程的方法：递推法、特征方程法和生成函数法。这3种方法基本上可以解决一般规模递归方程的求解问题。     

算法时间复杂度分析中递归方程求解方法综述

算法分析中计算复杂性常用递归关系来表达,递归方程的求解有助于分析算法设计的好坏。常用的递归方程的求解方法包括生成函数法、特征方程法、递推法等。递归树方法和主方法给出了递归方程计算复杂度的渐进表示。     

递归问题的递归分析

从生活化的递归现象、数学化的递归公式、程序化的递归方法等三个层次,分析了递归问题的关键思维特征、数学递归模型和程序设计方法,并提出递归方法应用模式,最后应用该模式求解典型的递归问题。     

数据结构中递归算法的描述与实现

通过数据结构理论与实验教学中的典型实例,论述了数据结构中递归算法的执行过程、递归算法的描述、应用、递归算法的非递归实现问题和递归算法的具体实现问题。     

汉诺塔问题的计算机辅助教学

递归问题是数据结构教学中的一个重要内容,递归算法在理解上有一定的难度,其教学方法对学生正确理解和应用递归解决实际问题是一个关键。汉诺塔问题是用递归方法求解的一个典型问题,在实际教学中,可以在传统教学方式的基础上,利用计算机辅助教学进行算法的模拟演示教学,使学生更容易接受和理解递归算法的思想,取得较好的教学效果。     

数据结构中递归算法的描述与实现

通过数据结构理论与实验教学中的典型实例,论述了数据结构中递归算法的执行过程、递归算法的描述、应用、递归算法的非递归实现问题和递归算法的具体实现问题.     

基于特征方程的递推型数列通项的求解

本文讨论了整式一阶递推数列、整式二阶递推数列和分式型递推数列的通项求解问题,利用了特征方程求解法解决了递推数列的通项求解问题。     

基于特征方程的递推型数列通项的求解

本文讨论了整式一阶递推数列、整式二阶递推数列和分式型递推数列的通项求解问题,利用了特征方程求解法解决了递推数列的通项求解问题。     

浅析程序设计中的递归算法

文章阐述了递归算法的本质及解决问题的思路。通过实例,对递归算法的执行过程进行了分析,并对递归算法的非递归化作了分析和探讨。     

数据结构课程中递归算法教学探讨

数据结构课程中的递归算法的教学既是重点又是难点.在教学中,教师可以提前引入递归算法,在讲授某些比较简单的问题的非递归算法时,补充递归算法,为比较复杂的问题的递归算法的教学铺平道路.采用该方法后,递归算法的教学取得了较好的效果.     

递归思想和形象思维在概率论教学中的应用

本文利用递归思想解决初等概率论中的一些难题．并利用形象思维的方式来理解现代概率论中的高度抽象的条件期望。     

Design of 2-D stable analog and recursive digital filters using properties of the derivative of even or odd Parts of Hurwitz polynomials

In this paper, a method for the design of 2-D analog and recursive digital filters is presented. Starting from a structure in the analog domain, suitable even or odd parts of two-variable Hurwitz polynomials are generated. This enables 2-variable very strictly Hurwitz polynomials (VSHP) to be obtained,² thus avoiding non-essential singularities of the second kind. Thus it will ensure a stable 2-D recursive digital filter obtained by the use of bilinear transformations. Examples are given to illustrate the method.     

黑河上游地区基流分割及其变化特征分析

基流是枯水期河川径流的主要来源,是一种比较稳定的径流组成部分,对于干旱内流河流域水文模拟和水资源开发利用至关重要。本文基于1979年-2008年莺落峡水文站的实测流量资料,采用数字滤波法中的单参数数字滤波法和递归数字滤波法对内陆河流域黑河上游的流量过程进行了基流分割研究。探讨了黑河上游年基流量和基流指数BFI的年内与年际变化特征,以及不同水平年基流指数BFI变化规律。研究表明,黑河上游基流量年内变化为先增后减,峰值出现在8月份,基流指数则是先减后增,6月份最小。受气温升高和融雪径流影响,黑河上游基流量年际变化呈增加趋势,而基流指数呈减少趋势。在不同水平年,枯水年份的平均基流指数BFI为O．577,平水年为0．551,丰水年为0．521。     

Auxiliary model based recursive generalized least squares identification algorithm for multivariate output-error autoregressive systems using the decomposition technique

This paper focuses on the parameter estimation problem of multivariate output-error autoregressive systems. Based on the decomposition technique and the auxiliary model identification idea, we derive a decomposition based auxiliary model recursive generalized least squares algorithm. The key is to divide the system into two fictitious subsystems, the one including a parameter vector and the other including a parameter matrix, and to estimate the two subsystems using the recursive least squares method, respectively. Compared with the auxiliary model based recursive generalized least squares algorithm, the proposed algorithm has less computational burden. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithms.     

Control systems approach to the sample inverse covariance matrix

A new method is proposed for finding the inverse of the covariance (or correlation) matrix. The technique is based on a previous method known as automatic variance control. The technique naturally gives rise to the inverse due to the properties of negative feedback itself rather than by traditional invertion methods. The method can be applied to the non-stationary problem and can form part of a recursive parameter estimation scheme.     

动态规划法在程序设计中的应用

探讨动态规划法的本质及在计算机程序设计中的应用。提出求解Fibonacci序列的3种算法,即递归法、自底向上和自顶向下动态规划法,证明将动态规划法用于程序设计,能降低算法的时间复杂度和空间复杂度。     

Probability-constrained tracking control for a class of time-varying nonlinear stochastic systems

This paper is concerned with the probability-constrained tracking control problem for a class of time-varying systems with stochastic nonlinearities, stochastic noises and successively packet loss. The main purpose of this paper is to design a time-varying observer and tracking controller such that (1) the probabilities of both the estimation error and tracking error confined to given ellipsoidal sets are larger than prescribed constants, and (2) the ellipsoids are minimized in the sense of matrix norm at each time point. By using a stochastic analysis method, the probability constrained tracking control problem is solved and sufficient conditions are obtained in terms of recursive linear matrix inequalities. A recursive optimization algorithm is developed to design the observer and tracking controller such that not only the addressed probability constrained aim is satisfied, but also the ellipsoidal sets are minimized. At last, a simulation example is given to illustrate the effectiveness and applicability of the developed approach.     

Robust identification of linear ARX models with recursive EM algorithm based on Student’s t-distribution

This paper considers the robust identification issue of linear systems represented by autoregressive exogenous models using the recursive expectation-maximization (EM) algorithm. In this paper, a recursive Q-function is formulated based on the maximum likelihood principle. Meanwhile, the outliers that frequently appear in practical processes are accommodated with the Student’s t-distribution. The parameter vector, variance of noise, and the degree of freedom are recursively estimated. Finally, a numerical example, as well as a simulated continuous stirred tank reactor (CSTR) system, is performed to verify the effectiveness of the proposed recursive EM algorithm.