Let f : X --> R-k be a Lipschitz continuous function on a compact subset X subset of R-d. subdivision algorithms are described that can be used to find all solutions of the equation f(x) = 0 that lie in X, Converge...
详细信息
Let f : X --> R-k be a Lipschitz continuous function on a compact subset X subset of R-d. subdivision algorithms are described that can be used to find all solutions of the equation f(x) = 0 that lie in X, Convergence is shown and numerical examples are presented. Modifications of the basic algorithm which speed convergence are given for the case of nondegenerate zeros of a vector field. (C) 2001 Elsevier Science B.V. All rights reserved.
A class of generalized moving average operators is introduced, and the integral representations of an average function are provided. It has been shown that the average of Dirac δ distribution is just the well kn...
详细信息
A class of generalized moving average operators is introduced, and the integral representations of an average function are provided. It has been shown that the average of Dirac δ distribution is just the well known box spline. Some remarks on box splines, such as their smoothness and the corresponding partition of unity, are made. The factorization of average operators is derived. Then, the subdivision algorithm for efficient computing of box splines and their linear combinations follows.
Different methods for the approximation of a set of data points with interpolatory property and appropriate boundary conditions are investigated with respect to the exact energy value. It is found that for a given set...
详细信息
Different methods for the approximation of a set of data points with interpolatory property and appropriate boundary conditions are investigated with respect to the exact energy value. It is found that for a given set of data points on a plane, the 6-point interpolatory subdivision method could be the best choice among the current widely used methods such as cubic splines and exponential splines due to its simplicity, locality, efficiency and most of all, its near-minimum energy property. Examples and graphics are provided to show these properties of the curves produced by the subdivision algorithm. (C) 2000 Elsevier Science Inc. All rights reserved.
Using the ideas employed in the construction of subdivision algorithms, we offer here a high-accuracy algorithm to compute numerical solutions for two point boundary-value problems of differential equations with devia...
详细信息
Using the ideas employed in the construction of subdivision algorithms, we offer here a high-accuracy algorithm to compute numerical solutions for two point boundary-value problems of differential equations with deviating arguments. Numerical examples are included to demonstrate the fast convergence and high accuracy of the algorithm. This paper is a further development to our previous works for solving various types of boundary-value problems. (C) 1998 Elsevier Science Ltd. All rights reserved.
The method of Dubuc and Deslauriers on symmetric interpolatory subdivision is extended to study the relationship between interpolation processes and wavelet construction. Refinable and interpolatory functions are cons...
详细信息
The method of Dubuc and Deslauriers on symmetric interpolatory subdivision is extended to study the relationship between interpolation processes and wavelet construction. Refinable and interpolatory functions are constructed in stages from B-splines. Their method constructs the filter sequence (its Laurent polynomial) of the interpolatory function as a product of Laurent polynomials. This provides a natural way of splitting the filter for the construction of orthonormal and biorthogonal scaling functions leading to orthonormal and biorthogonal wavelets. Their method also leads to a class of filters which includes the minimal length Daubechies compactly supported orthonormal wavelet coefficients. Examples of ''good'' filters are given together with results of numerical experiments conducted to test the performance of these filters in data compression. (C) 1998 Academic Press.
In this paper, an iterative algorithm for serving singular nonlinear two-point boundary value problems is formulated. This method is basically a collocation method for nonlinear second-order two-point boundary value p...
详细信息
In this paper, an iterative algorithm for serving singular nonlinear two-point boundary value problems is formulated. This method is basically a collocation method for nonlinear second-order two-point boundary value problems with singularities at either one or both of the boundary points. It is proved that the iterative algorithm converges to a smooth approximate solution of the BVP provided the boundary value problem is well posed and the algorithm is applied appropriately. Error estimates for uniform partitions are also investigated. It has been shown that, for sufficiently smooth solutions, the method produces order h(4) approximations. Numerical examples are provided to show the effectiveness of the algorithm.
In this paper, by using the ideas employed in the analysis of interpolatory subdivision algorithms for the generation of smooth curves, an iterative scheme for solving nonlinear two point boundary value problems is fo...
详细信息
In this paper, by using the ideas employed in the analysis of interpolatory subdivision algorithms for the generation of smooth curves, an iterative scheme for solving nonlinear two point boundary value problems is formulated. This method is basically a collocation method for nonlinear second order two point boundary value problems. It is proved that the iterative algorithm converges to a smooth approximate solution provided the boundary value problem is well posed and the algorithm is applied appropriately. Error estimates in the case of uniform partitions are also investigated. Some numerical examples are included to show the convergence of the proposed algorithm.
A special class of basis functions generated by uniform subdivision algorithms is used to formulate a high accuracy algorithm for the computation of approximate solutions of general two point boundary value problems o...
详细信息
A special class of basis functions generated by uniform subdivision algorithms is used to formulate a high accuracy algorithm for the computation of approximate solutions of general two point boundary value problems of differential equations with or without deviating arguments. This approach, which is different from the traditional finite difference or finite element method, produces non-polynomial/non-spline type, but continuous and differentiable approximate solutions to the boundary value problems provided the parameters of the algorithm are chosen appropriately. The main ideas of the method are generation of basis functions, node collocation, and boundary treatments. Numerical examples of various types of non-linear two-point boundary value problems are included to show the fast convergence and high accuracy of the algorithm. This paper is a further development of our previous work for solving linear boundary value problems and boundary value problems with deviating arguments.
Smooth interpolatory subdivision algorithms for the generation of curves are used to solve two point boundary value problems. A method of collocation is formulated for linear second order two point boundary value prob...
详细信息
Smooth interpolatory subdivision algorithms for the generation of curves are used to solve two point boundary value problems. A method of collocation is formulated for linear second order two point boundary value problems. It is proved that the algorithms produce smooth continuous solutions provided the algorithms are chosen appropriately. Error estimates for uniform partitions are also investigated. Finally, some numerical examples are given to show the convergence of the algorithms.
In this paper, a smooth interpolatory subdivision algorithm for the generation of interpolatory surfaces (GC(1)) over arbitrary triangulations is constructed and its convergence properties over nonuniform triangulatio...
详细信息
In this paper, a smooth interpolatory subdivision algorithm for the generation of interpolatory surfaces (GC(1)) over arbitrary triangulations is constructed and its convergence properties over nonuniform triangulations studied. An immediate application of this algorithm to surface interpolation to scattered data in R(n), n greater than or equal to 3 is also studied. For uniform data, this method is a generalization of the analyses for univariate subdivision algorithms, and for nonuniform data, an extraordinary point analysis is proposed and a local subdivision matrix analysis presented. (-)It is proved that the subdivision algorithm produces smooth surfaces over arbitrary networks provided the shape parameters of the algorithm are kept within an appropriate range. Some error estimates for both uniform and nonuniform triangulations are also investigated. Finally, three graphical examples of surface interpolations over nonuniform data are given to show the smoothing interpolating process of the algorithm.
暂无评论