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A comparison of piecewise cubic Hermite interpolating polynomials,cubic splines and piecewise linear functions for the approximation of projectile aerodynamics 被引量:3
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作者 C.A.Rabbath D.Corriveau 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2019年第5期741-757,共17页
Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and repr... Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile. 展开更多
关键词 Aerodynamic coefficients PIECEWISE POLYNOMIAL functionS CUBIC splines Curve fitting PIECEWISE linear functionS PIECEWISE CUBIC HERMITE interpolating POLYNOMIAL PROJECTILE modelling and simulation Fire control inputs Precision Ballistic computer software
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UNIVERSAL INTERPOLATING SEQUENCES ON SPACES OF ANALYTIC FUNCTIONS 被引量:1
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作者 B.Yousefi 《Acta Mathematica Scientia》 SCIE CSCD 2011年第1期68-72,共5页
This article derives the relation between universal interpolating sequences and some spectral properties of the multiplication operator by the independent variable z in case the underlying space is a Hilbert space of ... This article derives the relation between universal interpolating sequences and some spectral properties of the multiplication operator by the independent variable z in case the underlying space is a Hilbert space of functions analytic on the open unit disk. 展开更多
关键词 Hilbert spaces of analytic functions universal interpolating sequence multiplication operator invariant subspaces spectral properties
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SIMULTANEOUSE APPROXIMATION TO A DIFFERENTIABLE FUNCTION AND ITS DERIVATIVES BY LAGRANGE INTERPOLATING POLYNOMIALS 被引量:1
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作者 T.F.Xie S.P.Zhou 《Analysis in Theory and Applications》 1994年第4期100-109,共10页
This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of... This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of deereeon the nodes X_nUY_n(see the definition of the next). 展开更多
关键词 SIMULTANEOUSE APPROXIMATION TO A DIFFERENTIABLE function AND ITS DERIVATIVES BY LAGRANGE interpolating POLYNOMIALS APPI ZR
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Reconstruction of B-spline surface by interpolating boundary curves and approximating inner points 被引量:2
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作者 Mu Guowan and Dai Shijie 《Computer Aided Drafting,Design and Manufacturing》 2012年第1期31-34,共4页
In this paper, we present an algorithm for reconstruction of B-spline surface such that it interpolates the four given bound- ary curves and simultaneously approximates some given inner points. The main idea of our me... In this paper, we present an algorithm for reconstruction of B-spline surface such that it interpolates the four given bound- ary curves and simultaneously approximates some given inner points. The main idea of our method is: first, we construct an initial surface which interpolates the four given boundary curves; then, while keeping the boundary control points of the initial surface un- changed, we reposition the inner control points of the surface with energy optimization method. Examples show that our algorithm is practicable and effective. 展开更多
关键词 surface reconstruction b-spline interpolATION APPROXIMATION optimization
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A Hybrid Level Set Optimization Design Method of Functionally Graded Cellular Structures Considering Connectivity
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作者 Yan Dong Kang Zhao +1 位作者 Liang Gao Hao Li 《Computers, Materials & Continua》 SCIE EI 2024年第4期1-18,共18页
With the continuous advancement in topology optimization and additive manufacturing(AM)technology,the capability to fabricate functionally graded materials and intricate cellular structures with spatially varying micr... With the continuous advancement in topology optimization and additive manufacturing(AM)technology,the capability to fabricate functionally graded materials and intricate cellular structures with spatially varying microstructures has grown significantly.However,a critical challenge is encountered in the design of these structures–the absence of robust interface connections between adjacent microstructures,potentially resulting in diminished efficiency or macroscopic failure.A Hybrid Level Set Method(HLSM)is proposed,specifically designed to enhance connectivity among non-uniform microstructures,contributing to the design of functionally graded cellular structures.The HLSM introduces a pioneering algorithm for effectively blending heterogeneous microstructure interfaces.Initially,an interpolation algorithm is presented to construct transition microstructures seamlessly connected on both sides.Subsequently,the algorithm enables the morphing of non-uniform unit cells to seamlessly adapt to interconnected adjacent microstructures.The method,seamlessly integrated into a multi-scale topology optimization framework using the level set method,exhibits its efficacy through numerical examples,showcasing its prowess in optimizing 2D and 3D functionally graded materials(FGM)and multi-scale topology optimization.In essence,the pressing issue of interface connections in complex structure design is not only addressed but also a robust methodology is introduced,substantiated by numerical evidence,advancing optimization capabilities in the realm of functionally graded materials and cellular structures. 展开更多
关键词 Hybrid level set method functionally graded cellular structure CONNECTIVITY interpolated transition optimization design
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Radial Basis Function Based Implicit Surface Reconstruction Interpolating Arbitrary Triangular Mesh
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作者 PANG Mingyong (Department of Educational Technology,Nanjing Normal University,Nanjing 210097,China 《武汉理工大学学报》 CAS CSCD 北大核心 2006年第S2期586-591,共6页
In this paper,we present an approach for smooth surface reconstructions interpolating triangular meshes with ar- bitrary topology and geometry.The approach is based on the well-known radial basis functions (RBFs) and ... In this paper,we present an approach for smooth surface reconstructions interpolating triangular meshes with ar- bitrary topology and geometry.The approach is based on the well-known radial basis functions (RBFs) and the constructed surfaces are generalized thin-plate spline surfaces.Our algorithm first defines a pair of offset points for each vertex of a given mesh to en- hance the controUability of local geometry and to assure stability of the construction.A linear system is then solved by LU decomposi- tion and the implicit governing equation of interpolating surface is obtained.The constructed surfaces finally are visualized by a Marching Cubes based polygonizer.The approach provides a robust and efficient solution for smooth surface reconstruction from various 3 D meshes. 展开更多
关键词 IMPLICIT SURFACE SURFACE RECONSTRUCTION RADIAL BASIS function interpolating SURFACE
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A CONVERGENCE THEOREM ON THE MULTIVARIATE INTERPOLATING RATIONAL FUNCTIONS
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作者 宋宝瑞 《Journal of Shanghai Jiaotong university(Science)》 EI 1999年第2期59-63,共5页
This paper investigated the convergence of the columns (with fixed denominator degrees) of the multivariate rational interpolations to a meromorphic function. A simple convergence criterion and the rate of convergence... This paper investigated the convergence of the columns (with fixed denominator degrees) of the multivariate rational interpolations to a meromorphic function. A simple convergence criterion and the rate of convergence were given. The criterion is a nature extension of the theorem of Saff for the convergence of columns of univariate rational interpolations. 展开更多
关键词 RATIONAL interpolATION CONVERGENCE MULTIVARIATE MEROMORPHIC functionS
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Analysis of radial basis function interpolation approach 被引量:4
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作者 邹友龙 胡法龙 +3 位作者 周灿灿 李潮流 李长喜 Keh-Jim Dunn 《Applied Geophysics》 SCIE CSCD 2013年第4期397-410,511,共15页
The radial basis function (RBF) interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical prop... The radial basis function (RBF) interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman's RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart. 展开更多
关键词 Inverse problems radial basis function interpolation new approach
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DIMENSION AND DIFFERENTIABILIIY OF A CLASS OF FRACTAL INTERPOLATION FUNCTIONS 被引量:2
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作者 WANG GUOZHONG Department of Mathematics, Zhejiang University Hangzhou 310027 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1996年第1期85-100,共16页
In this paper, a new iterated function system consisting of non-linear affinemaps is constructed. We investigate the fractal interpolation functions generated bysuch a system and get its differentiability, its box dim... In this paper, a new iterated function system consisting of non-linear affinemaps is constructed. We investigate the fractal interpolation functions generated bysuch a system and get its differentiability, its box dimension, its packing dimension,and a lower bound of its Hansdorff dimension. 展开更多
关键词 FRACTAL interpolation function DIMENSION DIFFERENTIABILITY
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THE SMOOTHNESS AND DIMENSION OF FRACTAL INTERPOLATION FUNCTIONS 被引量:2
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作者 CHENGANG 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1996年第4期409-418,共10页
TheSmoothnesandDimensionofFractalInterpolationFunctions*ChenGangabstract.Inthispaper,weinvestigatethesmoothn... TheSmoothnesandDimensionofFractalInterpolationFunctions*ChenGangabstract.Inthispaper,weinvestigatethesmoothnessofnon-equidist... 展开更多
关键词 and FRACTAL functionS interpolATION Smoothnes DIMENSION
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On cubic Hermite coalescence hidden variable fractal interpolation functions 被引量:1
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作者 Puthan Veedu Viswanathan Arya Kumar Bedabrata Chand 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2015年第1期55-76,共22页
Hermite interpolation is a very important tool in approximation theory and nu- merical analysis, and provides a popular method for modeling in the area of computer aided geometric design. However, the classical Hermit... Hermite interpolation is a very important tool in approximation theory and nu- merical analysis, and provides a popular method for modeling in the area of computer aided geometric design. However, the classical Hermite interpolant is unique for a prescribed data set, and hence lacks freedom for the choice of an interpolating curve, which is a crucial requirement in design environment. Even though there is a rather well developed fractal theory for Hermite interpolation that offers a large flexibility in the choice of interpolants, it also has the short- coming that the functions that can be well approximated are highly restricted to the class of self-affine functions. The primary objective of this paper is to suggest a gl-cubic Hermite in- terpolation scheme using a fractal methodology, namely, the coalescence hidden variable fractal interpolation, which works equally well for the approximation of a self-affine and non-self-affine data generating functions. The uniform error bound for the proposed fractal interpolant is established to demonstrate that the convergence properties are similar to that of the classical Hermite interpolant. For the Hermite interpolation problem, if the derivative values are not actually prescribed at the knots, then we assign these values so that the interpolant gains global G2-continuity. Consequently, the procedure culminates with the construction of cubic spline coalescence hidden variable fractal interpolants. Thus, the present article also provides an al- ternative to the construction of cubic spline coalescence hidden variable fractal interpolation functions through moments proposed by Chand and Kapoor [Fractals, 15(1) (2007), pp. 41-53]. 展开更多
关键词 cubic Hermite interpolant cubic spline fractal interpolation function COALESCENCE hidden vari-able convergence.
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Hermite interpolation and its numerical differentiation formula involving symmetric functions 被引量:1
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作者 BAI Hong-huan XU Ai-min 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2009年第3期309-314,共6页
By utilizing symmetric functions,this paper presents explicit representations for Hermite interpolation and its numerical differentiation formula.And the corresponding error estimates are also provided.
关键词 Hermite interpolation numerical differentiation elementary symmetric function complete symmetric function
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2-D NONSEPARABLE SCALING FUNCTIONINTERPOLATION AND APPROXIMATION 被引量:1
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作者 En-Bing, Lin Yi Ling (Department of Mathematics. University of Toledo, Toledo, OH .43606, USA) 《Acta Mathematica Scientia》 SCIE CSCD 2002年第1期19-31,共13页
The authors introduce nonseparable scaling function interpolation and show that its approximation can provide similar convergence properties as scalar wavelet system. Several equivalent statements of accuracy of nonse... The authors introduce nonseparable scaling function interpolation and show that its approximation can provide similar convergence properties as scalar wavelet system. Several equivalent statements of accuracy of nonseparable scaling function are also given. In the numerical experiments, it appears that nonseparable scaling function interpolation has better convergence results than scalar wavelet systems in some cases. 展开更多
关键词 WAVELETS nonseparable scaling function interpolATION accuracy of scaling function. 2-D MRA
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HERMITE—BIRKHOFF INTERPOLATION OF SCATTERED DATA BY RADIAL BASIS FUNCTIONS 被引量:6
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作者 吴宗敏 《Analysis in Theory and Applications》 1992年第2期1-10,共10页
For Hermite-Birkhoff interpolation of scattered multidumensional data by radial basis function (?),existence and characterization theorems and a variational principle are proved. Examples include (?)(r)=r^b,Duchon'... For Hermite-Birkhoff interpolation of scattered multidumensional data by radial basis function (?),existence and characterization theorems and a variational principle are proved. Examples include (?)(r)=r^b,Duchon's thin-plate splines,Hardy's multiquadrics,and inverse multiquadrics. 展开更多
关键词 HERMITE BIRKHOFF interpolATION OF SCATTERED DATA BY RADIAL BASIS functionS
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HOLDER PROPERTY OF FRACTAL INTERPOLATION FUNCTION 被引量:3
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作者 沙震 《Analysis in Theory and Applications》 1992年第4期45-57,共13页
The purpose of this paper is to prove a Holder property about the fractal interpolation function L(x), ω(L,δ)=O(δ~α), and an approximate estimate |f-L|≤2{α(h)+||f||/1-h^(2-D)·h^(2-D)}, where D is a fractal ... The purpose of this paper is to prove a Holder property about the fractal interpolation function L(x), ω(L,δ)=O(δ~α), and an approximate estimate |f-L|≤2{α(h)+||f||/1-h^(2-D)·h^(2-D)}, where D is a fractal dimension of L(x). 展开更多
关键词 PRO IL HOLDER PROPERTY OF FRACTAL interpolATION function
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Performance of global look-up table strategy in digital image correlation with cubic B-spline interpolation and bicubic interpolation 被引量:4
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作者 Zhiwei Pan Wei Chen +3 位作者 Zhenyu Jiang Liqun Tang Yiping Liu Zejia Liu 《Theoretical & Applied Mechanics Letters》 CAS CSCD 2016年第3期126-130,共5页
Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation (... Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation (DIC) algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss-Newton (IC-GN) algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency. 展开更多
关键词 Digital image correlation Inverse compositional Gauss-Newton algorithm Cubic b-spline interpolation Bicubic interpolation Global look-up table
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Interpolating Isogeometric Boundary Node Method and Isogeometric Boundary Element Method Based on Parameter Space 被引量:1
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作者 Hongyin Yang Jiwei Zhong +2 位作者 Ying Wang Xingquan Chen Xiaoya Bian 《Computer Modeling in Engineering & Sciences》 SCIE EI 2020年第9期807-824,共18页
In this paper,general interpolating isogeometric boundary node method(IIBNM)and isogeometric boundary element method(IBEM)based on parameter space are proposed for 2D elasticity problems.In both methods,the integral c... In this paper,general interpolating isogeometric boundary node method(IIBNM)and isogeometric boundary element method(IBEM)based on parameter space are proposed for 2D elasticity problems.In both methods,the integral cells and elements are defined in parameter space,which can reproduce the geometry exactly at all the stages.In IIBNM,the improved interpolating moving leastsquare method(IIMLS)is applied for field approximation and the shape functions have the delta function property.The Lagrangian basis functions are used for field approximation in IBEM.Thus,the boundary conditions can be imposed directly in both methods.The shape functions are defined in 1D parameter space and no curve length needs to be computed.Besides,most methods for the treatment of the singular integrals in the boundary element method can be applied in IIBNM and IBEM directly.Numerical examples have demonstrated the accuracy of the proposed methods. 展开更多
关键词 interpolating isogeometric boundary node method isogeometric boundary element method parameter space improved interpolating moving least-square method Lagrangian basis functions
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Radial Basis Function Interpolation and Galerkin Projection for Direct Trajectory Optimization and Costate Estimation 被引量:1
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作者 Hossein Mirinejad Tamer Inanc Jacek M.Zurada 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2021年第8期1380-1388,共9页
This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to... This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to optimal control problems,especially nonsmooth problems involving discontinuities,while accounting for trajectory accuracy and computational efficiency simultaneously.The proposed solution,called the RBF-Galerkin method,offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of points.The RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush-Kuhn-Tucker(KKT)conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem,if a set of discrete conditions holds.The efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control problem.In addition,the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency. 展开更多
关键词 Costate estimation direct trajectory optimization Galerkin projection numerical optimal control radial basis function interpolation
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PARAMETER IDENTIFICATION PROBLEM OF THE FRACTAL INTERPOLATION FUNCTIONS 被引量:4
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作者 阮火军 沙震 苏维宜 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2003年第2期205-213,共9页
Parameter identification problem is one of essential problem in order to model effectively experimental data by fractal interpolation function.In this paper,we first present an example to explain a relationship betwee... Parameter identification problem is one of essential problem in order to model effectively experimental data by fractal interpolation function.In this paper,we first present an example to explain a relationship between iteration procedure and fractal function.Then we discuss conditions that vertical scaling factors must obey in one typical case. 展开更多
关键词 分形插值函数 参数鉴定 吸引子 垂直定标因数
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HAAR EXPANSIONS OF A CLASS OF FRACTAL INTERPOLATION FUNCTIONS AND THEIR LOGICAL DERIVATIVES 被引量:1
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作者 Sha Zhen Chen Gang Zhejiang University,China 《Analysis in Theory and Applications》 1993年第4期73-88,共16页
In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their... In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α. 展开更多
关键词 HAAR EXPANSIONS OF A CLASS OF FRACTAL interpolATION functionS AND THEIR LOGICAL DERIVATIVES der HAAR FIF
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