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
It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy.The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of ...It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy.The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of q-shift operator θ, which originates from the Leibnitz rule of the quantum calculus. We further show that the n-reduction leads to a recursive scheme for these flow equations. The recursion operator for the flow equations of the q-KP hierarchy under the n-reduction is also derived.展开更多
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Supported by the National Natural Science Foundation of China under Grant Nos.11271210 and 11201451Anhui Province Natural Science Foundation under Grant No.1608085MA04
文摘It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy.The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of q-shift operator θ, which originates from the Leibnitz rule of the quantum calculus. We further show that the n-reduction leads to a recursive scheme for these flow equations. The recursion operator for the flow equations of the q-KP hierarchy under the n-reduction is also derived.
