Search results for: Chebyshev interpolation.

Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

This paper discusses a design of nonlinear observer by a formal linearization method using an application of Chebyshev Interpolation in order to facilitate processes for synthesizing a nonlinear observer and to improve the precision of linearization. A dynamic nonlinear system is linearized with respect to a linearization function, and a measurement equation is transformed into an augmented linear one by the formal linearization method which is based on Chebyshev interpolation. To the linearized system, a linear estimation theory is applied and a nonlinear observer is derived. To show effectiveness of the observer design, numerical experiments are illustrated and they indicate that the design shows remarkable performances for nonlinear systems.

Keywords: nonlinear system, nonlinear observer, formal linearization, Chebyshev interpolation.

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Authors: Mohammed A. Abutheraa, David Lester

Abstract:

We show that Chebyshev Polynomials are a practical representation of computable functions on the computable reals. The paper presents error estimates for common operations and demonstrates that Chebyshev Polynomial methods would be more efficient than Taylor Series methods for evaluation of transcendental functions.

Keywords: Approximation Theory, Chebyshev Polynomial, Computable Functions, Computable Real Arithmetic, Integration, Numerical Analysis.

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Authors: Junghan Kim, Wonkyu Chung, Sunyoung Bu, Philsu Kim

Abstract:

In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower degree polynomial. The constructed algorithm controls both the error and the time step size simultaneously and further the errors at each integration step are embedded in the algorithm itself, which provides the efficiency of the computational cost. For the assessment of the effectiveness, numerical results obtained by the proposed method and the Radau IIA are presented and compared.

Keywords: Generalized Chebyshev Collocation method, Generalized Chebyshev Polynomial, Initial value problem.

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Authors: M. Abdulkawi, Z. K. Eshkuvatov, N. M. A. Nik Long

Abstract:

This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.

Keywords: Singular integral equations, Cauchy kernel, Chebyshev polynomials, interpolation.

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Authors: Rongli Gai, Zhiyuan Chang, Xiaohong Wang, Jingyu Liu

Abstract:

In view of various situations in the interpolation process, most researchers use self-adaptation to adjust the interpolation process, which is also one of the current and future research hotspots in the field of CNC (Computerized Numerical Control) machining. In the interpolation process, according to the overview of the spline curve interpolation algorithm, the adaptive analysis is carried out from the factors affecting the interpolation process. The adaptive operation is reflected in various aspects, such as speed, parameters, errors, nodes, feed rates, random period, sensitive point, step size, curvature, adaptive segmentation, adaptive optimization, etc. This paper will analyze and summarize the research of adaptive imputation in the direction of the above factors affecting imputation.

Keywords: Adaptive algorithm, CNC machining, interpolation constraints, spline curve interpolation.

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Authors: Vinod Mishra, Dimple Rani

Abstract:

In this paper, numerical approximate Laplace transform inversion algorithm based on Chebyshev polynomial of second kind is developed using odd cosine series. The technique has been tested for three different functions to work efficiently. The illustrations show that the new developed numerical inverse Laplace transform is very much close to the classical analytic inverse Laplace transform.

Keywords: Chebyshev polynomial, Numerical inverse Laplace transform, Odd cosine series.

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Authors: A. Pashayev, C. Ardil, R. Sadiqov

Abstract:

Various methods of geofield parameters restoration (by algebraic polynoms; filters; rational fractions; interpolation splines; geostatistical methods – kriging; search methods of nearest points – inverse distance, minimum curvature, local – polynomial interpolation; neural networks) have been analyzed and some possible mistakes arising during geofield surface modeling have been presented.

Keywords: interpolation methods, geofield parameters, neural networks.

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Authors: Srijanani Anurag Prasad

Abstract:

The Coalescence Hidden-variable Fractal Interpolation Surface (CHFIS) was built by combining interpolation data from the Iterated Function System (IFS). The interpolation data in a CHFIS comprise a row and/or column of uncertain values when a single point is entered. Alternatively, a row and/or column of additional points are placed in the given interpolation data to demonstrate the node added CHFIS. There are three techniques for inserting new points that correspond to the row and/or column of nodes inserted, and each method is further classified into four types based on the values of the inserted nodes. As a result, numerous forms of node insertion can be found in a CHFIS.

Keywords: Fractal, interpolation, iterated function system, coalescence, node insertion, knot insertion.

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Authors: Chuan Li, Ming Liang, Qibing Yu

Abstract:

To improve the dynamics response of the vehicle passive suspension, a two-terminal mass is suggested to connect in parallel with the suspension strut. Three performance criteria, tire grip, ride comfort and suspension deflection, are taken into consideration to optimize the suspension parameters. However, the three criteria are conflicting and non-commensurable. For this reason, the Chebyshev goal programming method is applied to find the best tradeoff among the three objectives. A simulation case is presented to describe the multi-objective optimization procedure. For comparison, the Chebyshev method is also employed to optimize the design of a conventional passive suspension. The effectiveness of the proposed design method has been clearly demonstrated by the result. It is also shown that the suspension with a two-terminal mass in parallel has better performance in terms of the three objectives.

Keywords: Vehicle, passive suspension, two-terminal mass, optimization, Chebyshev goal programming

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Authors: F. Castillo, J. Arellano, S. Sánchez

Abstract:

In this paper an alternative analysis in the time domain is described and the results of the interpolation process are presented by means of functions that are based on the rule of conditional mathematical expectation and the covariance function. A comparison between the interpolation error caused by low order filters and the classic sinc(t) truncated function is also presented. When fewer samples are used, low-order filters have less error. If the number of samples increases, the sinc(t) type functions are a better alternative. Generally speaking there is an optimal filter for each input signal which depends on the filter length and covariance function of the signal. A novel scheme of work for adaptive interpolation filters is also presented.

Keywords: Interpolation, basis function, over-sampling.

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Authors: Tarun Gulati, Kapil Gupta, Dushyant Gupta

Abstract:

High resolution images are always desired as they contain the more information and they can better represent the original data. So, to convert the low resolution image into high resolution interpolation is done. The quality of such high resolution image depends on the interpolation function and is assessed in terms of sharpness of image. This paper focuses on Wavelet based Interpolation Techniques in which an input image is divided into subbands. Each subband is processed separately and finally combined the processed subbandsto get the super resolution image. 

Keywords: SWT, DWTSR, DWTSWT, DWCWT.

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Authors: Yaoxin Zhang, Yafei Jia, Sam S.Y. Wang

Abstract:

A multi-block algorithm and its implementation in two-dimensional finite element numerical model CCHE2D are presented. In addition to a conventional Lagrangian Interpolation Method (LIM), a novel interpolation method, called Consistent Interpolation Method (CIM), is proposed for more accurate information transfer across the interfaces. The consistent interpolation solves the governing equations over the auxiliary elements constructed around the interpolation nodes using the same numerical scheme used for the internal computational nodes. With the CIM, the momentum conservation can be maintained as well as the mass conservation. An imbalance correction scheme is used to enforce the conservation laws (mass and momentum) across the interfaces. Comparisons of the LIM and the CIM are made using several flow simulation examples. It is shown that the proposed CIM is physically more accurate and produces satisfactory results efficiently.

Keywords: Multi-block algorithm, conservation, interpolation, numerical model, flow simulation.

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Authors: Mehdi Tatari

Abstract:

Finding the interpolation function of a given set of nodes is an important problem in scientific computing. In this work a kind of localization is introduced using the radial basis functions which finds a sufficiently smooth solution without consuming large amount of time and computer memory. Some examples will be presented to show the efficiency of the new method.

Keywords: Radial basis functions, local interpolation method, closed form solution.

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Authors: J. Kavikumar, N. S. Manian, M. B. K. Moorthy

Abstract:

The main purpose of this paper is to consider the new kind of approximation which is called as t-best coapproximation in fuzzy n-normed spaces. The set of all t-best coapproximation define the t-coproximinal, t-co-Chebyshev and F-best coapproximation and then prove several theorems pertaining to this sets. 

Keywords: Fuzzy-n-normed space, best coapproximation, co-proximinal, co-Chebyshev, F-best coapproximation, orthogonality

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Authors: Wang liguo, Wang zongmin, Kong ying

Abstract:

A novel interpolation scheme to extend usable spectrum and upconvert in high performance D/A converters is addressed in this paper. By adjusting the pulse width of cycle and the production circuit of code, the expansion code is a null code or complementary code that is interpolation process. What the times and codes of interpolation decide DAC works in one of a normal mode or multi-mixer mode so that convert the input digital data signal into normal signal or a mixed analog signal having a mixer frequency that is higher than the data frequency. Simulation results show that the novel scheme and apparatus most extend the usable frequency spectrum into fifth to sixth Nyquist zone beyond conventional DACs.

Keywords: interpolation, upconversion, modulation, switching function, duty cycle.

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Authors: Kourosh Parand, Zahra Delafkar, Fatemeh Baharifard

Abstract:

The problem of natural convection about a cone embedded in a porous medium at local Rayleigh numbers based on the boundary layer approximation and the Darcy-s law have been studied before. Similarity solutions for a full cone with the prescribed wall temperature or surface heat flux boundary conditions which is the power function of distance from the vertex of the inverted cone give us a third-order nonlinear differential equation. In this paper, an approximate method for solving higher-order ordinary differential equations is proposed. The approach is based on a rational Chebyshev Tau (RCT) method. The operational matrices of the derivative and product of rational Chebyshev (RC) functions are presented. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ordinary differential equations to the solution of a system of algebraic equations. We also present the comparison of this work with others and show that the present method is applicable.

Keywords: Tau method, semi-infinite, nonlinear ODE, rational Chebyshev, porous media.

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Authors: Hadi Taghvafard

Abstract:

We present a new quadrature rule based on the spline interpolation along with the error analysis. Moreover, some error estimates for the reminder when the integrand is either a Lipschitzian function, a function of bounded variation or a function whose derivative belongs to Lp are given. We also give some examples to show that, practically, the spline rule is better than the trapezoidal rule.

Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.

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Authors: Marzieh Dosti, Alireza Nazemi

Abstract:

In this paper, the telegraph equation is solved numerically by cubic B-spline quasi-interpolation .We obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable. The advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement. The results of numerical experiments are presented, and are compared with analytical solutions by calculating errors L2 and L∞ norms to confirm the good accuracy of the presented scheme.

Keywords: Cubic B-spline, quasi-interpolation, collocation method, second-order hyperbolic telegraph equation.

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Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang

Abstract:

Image interpolation is a common problem in imaging applications. However, most interpolation algorithms in existence suffer visually the effects of blurred edges and jagged artifacts in the image to some extent. This paper presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to sharpen edges along the normal directions to the isophote lines (edges), while a normal diffusion is done to remove artifacts (“jaggies") along the tangent directions. In order to preserve image features such as edges, corners and textures, the nonlinear diffusion coefficients are locally adjusted according to the directional derivatives of the image. Experimental results on synthetic images and nature images demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.

Keywords: anisotropic diffusion, bidirectional flow, directional derivatives, edge enhancement, image interpolation, inverse flow, shock filter.

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Authors: Rajeev, N. K. Raigar

Abstract:

In this study, one dimensional phase change problem (a Stefan problem) is considered and a numerical solution of this problem is discussed. First, we use similarity transformation to convert the governing equations into ordinary differential equations with its boundary conditions. The solutions of ordinary differential equation with the associated boundary conditions and interface condition (Stefan condition) are obtained by using a numerical approach based on operational matrix of differentiation of shifted second kind Chebyshev wavelets. The obtained results are compared with existing exact solution which is sufficiently accurate.

Keywords: Operational matrix of differentiation, Similarity transformation, Shifted second kind Chebyshev wavelets, Stefan problem.

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Authors: T. P. Athira, Gibin Chacko George

Abstract:

This paper proposes a dual tree complex wavelet transform (DT-CWT) based directional interpolation scheme for noisy images. The problems of denoising and interpolation are modelled as to estimate the noiseless and missing samples under the same framework of optimal estimation. Initially, DT-CWT is used to decompose an input low-resolution noisy image into low and high frequency subbands. The high-frequency subband images are interpolated by linear minimum mean square estimation (LMMSE) based interpolation, which preserves the edges of the interpolated images. For each noisy LR image sample, we compute multiple estimates of it along different directions and then fuse those directional estimates for a more accurate denoised LR image. The estimation parameters calculated in the denoising processing can be readily used to interpolate the missing samples. The inverse DT-CWT is applied on the denoised input and interpolated high frequency subband images to obtain the high resolution image. Compared with the conventional schemes that perform denoising and interpolation in tandem, the proposed DT-CWT based noisy image interpolation method can reduce many noise-caused interpolation artifacts and preserve well the image edge structures. The visual and quantitative results show that the proposed technique outperforms many of the existing denoising and interpolation methods.

Keywords: Dual-tree complex wavelet transform (DT-CWT), denoising, interpolation, optimal estimation, super resolution.

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Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang

Abstract:

Image interpolation is a common problem in imaging applications. However, most interpolation algorithms in existence suffer visually to some extent the effects of blurred edges and jagged artifacts in the image. This paper presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to enhance edges along the normal directions to the isophote lines (edges), while a normal diffusion is done to remove artifacts (''jaggies'') along the tangent directions. In order to preserve image features such as edges, angles and textures, the nonlinear diffusion coefficients are locally adjusted according to the first and second order directional derivatives of the image. Experimental results on synthetic images and nature images demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.

Keywords: anisotropic diffusion, bidirectional flow, directionalderivatives, edge enhancement, image interpolation, inverse flow, shock filter.

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Authors: Nur Nadiah Abd Hamid, Ahmad Abd. Majid, Ahmad Izani Md. Ismail

Abstract:

Linear two-point boundary value problem of order two is solved using extended cubic B-spline interpolation method. There is one free parameters, λ, that control the tension of the solution curve. For some λ, this method produced better results than cubic B-spline interpolation method.

Keywords: two-point boundary value problem, B-spline, extendedcubic B-spline.

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Authors: Muhanned Alfarras

Abstract:

The recent growth of using multimedia transmission over wireless communication systems, have challenges to protect the data from lost due to wireless channel effect. Images are corrupted due to the noise and fading when transmitted over wireless channel, in wireless channel the image is transmitted block by block, Due to severe fading, entire image blocks can be damaged. The aim of this paper comes out from need to enhance the digital images at the wireless receiver side. Proposed Boundary Interpolation (BI) Algorithm using wavelet, have been adapted here used to reconstruction the lost block in the image at the receiver depend on the correlation between the lost block and its neighbors. New Proposed technique by using Boundary Interpolation (BI) Algorithm using wavelet with Pixel interleaver has been implemented. Pixel interleaver work on distribute the pixel to new pixel position of original image before transmitting the image. The block lost through wireless channel is only effects individual pixel. The lost pixels at the receiver side can be recovered by using Boundary Interpolation (BI) Algorithm using wavelet. The results showed that the New proposed algorithm boundary interpolation (BI) using wavelet with pixel interleaver is better in term of MSE and PSNR.

Keywords: Image Transmission, Wavelet, Pixel Interleaver, Boundary Interpolation Algorithm

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Authors: Koushlendra Kumar Singh, Manish Kumar Bajpai, Rajesh K. Pandey

Abstract:

The edges of low contrast images are not clearly distinguishable to human eye. It is difficult to find the edges and boundaries in it. The present work encompasses a new approach for low contrast images. The Chebyshev polynomial based fractional order filter has been used for filtering operation on an image. The preprocessing has been performed by this filter on the input image. Laplacian of Gaussian method has been applied on preprocessed image for edge detection. The algorithm has been tested on two test images.

Keywords: Chebyshev polynomials, Fractional order differentiator, Laplacian of Gaussian (LoG) method, Low contrast image.

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Authors: Dragos Nicolae VIZIREANU

Abstract:

One of the main image representations in Mathematical Morphology is the 3D Shape Decomposition Representation, useful for Image Compression and Representation,and Pattern Recognition. The 3D Morphological Shape Decomposition representation can be generalized a number of times,to extend the scope of its algebraic characteristics as much as possible. With these generalizations, the Morphological Shape Decomposition 's role to serve as an efficient image decomposition tool is extended to grayscale images.This work follows the above line, and further develops it. Anew evolutionary branch is added to the 3D Morphological Shape Decomposition's development, by the introduction of a 3D Multi Structuring Element Morphological Shape Decomposition, which permits 3D Morphological Shape Decomposition of 3D binary images (grayscale images) into "multiparameter" families of elements. At the beginning, 3D Morphological Shape Decomposition representations are based only on "1 parameter" families of elements for image decomposition.This paper addresses the gray scale inter frame interpolation by means of mathematical morphology. The new interframe interpolation method is based on generalized morphological 3D Shape Decomposition. This article will present the theoretical background of the morphological interframe interpolation, deduce the new representation and show some application examples.Computer simulations could illustrate results.

Keywords: 3D shape decomposition representation, mathematical morphology, gray scale interframe interpolation

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Authors: Nur Nadiah Abd Hamid , Ahmad Abd. Majid, Ahmad Izani Md. Ismail

Abstract:

Linear two-point boundary value problems of order two are solved using cubic trigonometric B-spline interpolation method (CTBIM). Cubic trigonometric B-spline is a piecewise function consisting of trigonometric equations. This method is tested on some problems and the results are compared with cubic B-spline interpolation method (CBIM) from the literature. CTBIM is found to approximate the solution slightly more accurately than CBIM if the problems are trigonometric.

Keywords: trigonometric B-spline, two-point boundary valueproblem, spline interpolation, cubic spline

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Authors: Changqing Yang, Jianhua Hou, Beibo Qin

Abstract:

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equation into a system of algebraic equations. Corresponding numerical examples are presented to demonstrate the accuracy of the proposed method.

Keywords: Hybrid functions, Riccati differential equation, Blockpulse, Chebyshev polynomials, Tau method, operational matrix.

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Authors: jianhua Hou, Changqing Yang, and Beibo Qin

Abstract:

A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function  approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

Keywords: Hybrid functions, Fredholm integral equation, Blockpulse, Chebyshev polynomials, product operational matrix.

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Authors: Saeed Mian Qaisar, Laurent Fesquet, Marc Renaudin

Abstract:

Mostly the systems are dealing with time varying signals. The Power efficiency can be achieved by adapting the system activity according to the input signal variations. In this context an adaptive rate filtering technique, based on the level crossing sampling is devised. It adapts the sampling frequency and the filter order by following the input signal local variations. Thus, it correlates the processing activity with the signal variations. Interpolation is required in the proposed technique. A drastic reduction in the interpolation error is achieved by employing the symmetry during the interpolation process. Processing error of the proposed technique is calculated. The computational complexity of the proposed filtering technique is deduced and compared to the classical one. Results promise a significant gain of the computational efficiency and hence of the power consumption.

Keywords: Level Crossing Sampling, Activity Selection, Rate Filtering, Computational Complexity, Interpolation Error.

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