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
Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the...Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the FIF. Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) is both self-affine and non self-affine in nature depending on the free variables and constrained free variables for a generalized IFS. In this article, graph directed iterated function system for a finite number of generalized data sets is considered and it is shown that the projection of the attractors on is the graph of the CHFIFs interpolating the corresponding data sets.展开更多
INSITE(Integrated System for Information Technology and Engineering)软件是哈里伯顿公司支持其随钻测井服务的地面系统,其核心部分是一个庞大的开放式数据库(ODBC)连接的数据库系统。通过探索INSITE软件的隐藏功能,可以在广域网和...INSITE(Integrated System for Information Technology and Engineering)软件是哈里伯顿公司支持其随钻测井服务的地面系统,其核心部分是一个庞大的开放式数据库(ODBC)连接的数据库系统。通过探索INSITE软件的隐藏功能,可以在广域网和局域网内让全球INSITE工作站实时连接在一起,在任何地方都可以共享到这些数据库,从而实现24小时的实时监控,为现场作业提供强大的实时支持。主要介绍的随钻测井、测量相关模块的数据库原理。同时通过现场对隐藏功能的开发应用,实现现场作业难题的解决,减少因故障造成的经济损失。展开更多
In this paper we employ artificial neural networks for predictive approximation of generalized functions having crucial applications in different areas of science including mechanical and chemical engineering, signal ...In this paper we employ artificial neural networks for predictive approximation of generalized functions having crucial applications in different areas of science including mechanical and chemical engineering, signal processing, information transfer, telecommunications, finance, etc. Results of numerical analysis are discussed. It is shown that the known Gibb’s phenomenon does not occur.展开更多
基金partially supported by the CSIR India(Grant No.09/084(0531)/2010-EMR-I)the SERC,DST India(Project No.SR/S4/MS:694/10)
文摘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].
文摘Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the FIF. Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) is both self-affine and non self-affine in nature depending on the free variables and constrained free variables for a generalized IFS. In this article, graph directed iterated function system for a finite number of generalized data sets is considered and it is shown that the projection of the attractors on is the graph of the CHFIFs interpolating the corresponding data sets.
文摘INSITE(Integrated System for Information Technology and Engineering)软件是哈里伯顿公司支持其随钻测井服务的地面系统,其核心部分是一个庞大的开放式数据库(ODBC)连接的数据库系统。通过探索INSITE软件的隐藏功能,可以在广域网和局域网内让全球INSITE工作站实时连接在一起,在任何地方都可以共享到这些数据库,从而实现24小时的实时监控,为现场作业提供强大的实时支持。主要介绍的随钻测井、测量相关模块的数据库原理。同时通过现场对隐藏功能的开发应用,实现现场作业难题的解决,减少因故障造成的经济损失。
文摘In this paper we employ artificial neural networks for predictive approximation of generalized functions having crucial applications in different areas of science including mechanical and chemical engineering, signal processing, information transfer, telecommunications, finance, etc. Results of numerical analysis are discussed. It is shown that the known Gibb’s phenomenon does not occur.
