递归程序设计是《数据结构》中的一个难点,也是整个课程的重点之一。由于《数据结构》是软、硬件的专业基础课,对相关后继课程有相当的影响,所以应当对递归程序设计教学给予应有的重视。对于初学者,读懂递归过程、掌握它的动态执行过程...递归程序设计是《数据结构》中的一个难点,也是整个课程的重点之一。由于《数据结构》是软、硬件的专业基础课,对相关后继课程有相当的影响,所以应当对递归程序设计教学给予应有的重视。对于初学者,读懂递归过程、掌握它的动态执行过程是进行递归程序设计的第一步,是学好《数据结构》的关键之一。递归过程的定义学生们是能够接受的,而且对数学当中的递归函数(例如阶乘函数)和递归数列(例如 Fi-bonacci 数列)也是相当清楚的。而对于解决 n 阶 Hanoi 塔问题的递归过程,初学者就很难读懂了。展开更多
In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new ...In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new insertion control points on a finer grid are computed by weighted sums of already existing control points. In the limit of the recursive process, data is defined on a dense set of point, The objective is to find an improved subdivision approximating algorithm which has a smaller support and a higher approximating order. The author chooses a ternary scheme because the best way to get a smaller support is to pass from the binary to ternary or complex algorithm and uses polynomial reproducing propriety to get higher approximation order. Using the cardinal Lagrange polynomials the author has proposed a 4-point approximating ternary subdivision algorithm and found that a higher regularity of limit function does not guarantee a higher approximating order. The proposed 4-point ternary approximation subdivision family algorithms with the mask a have the limit function in C2 and have approximation order 4. Also the author has demonstrated that in this class there is no algorithm whose limit function is in C3. It can be seen that this stationary ternary 4-point approximating symmetrical subdivision algorithm has a lower computational cost than the 6-point binary approximation subdivision algorithm for a greater range of points.展开更多
I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is the...I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set.展开更多
文摘递归程序设计是《数据结构》中的一个难点,也是整个课程的重点之一。由于《数据结构》是软、硬件的专业基础课,对相关后继课程有相当的影响,所以应当对递归程序设计教学给予应有的重视。对于初学者,读懂递归过程、掌握它的动态执行过程是进行递归程序设计的第一步,是学好《数据结构》的关键之一。递归过程的定义学生们是能够接受的,而且对数学当中的递归函数(例如阶乘函数)和递归数列(例如 Fi-bonacci 数列)也是相当清楚的。而对于解决 n 阶 Hanoi 塔问题的递归过程,初学者就很难读懂了。
文摘In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new insertion control points on a finer grid are computed by weighted sums of already existing control points. In the limit of the recursive process, data is defined on a dense set of point, The objective is to find an improved subdivision approximating algorithm which has a smaller support and a higher approximating order. The author chooses a ternary scheme because the best way to get a smaller support is to pass from the binary to ternary or complex algorithm and uses polynomial reproducing propriety to get higher approximation order. Using the cardinal Lagrange polynomials the author has proposed a 4-point approximating ternary subdivision algorithm and found that a higher regularity of limit function does not guarantee a higher approximating order. The proposed 4-point ternary approximation subdivision family algorithms with the mask a have the limit function in C2 and have approximation order 4. Also the author has demonstrated that in this class there is no algorithm whose limit function is in C3. It can be seen that this stationary ternary 4-point approximating symmetrical subdivision algorithm has a lower computational cost than the 6-point binary approximation subdivision algorithm for a greater range of points.
基金Project supported by the National Natural Science Foundation of China the Doctoral Progamme Foundation of China and the Foundation of Wuhan University.
文摘I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set.
