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Approximate solutions of general nonlinear boundary value problems using subdivision techniques

ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 1997年第2C期22卷 121-135页

作者： Qu, RB Natl Univ Singapore Dept Math Singapore 119260 Singapore

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.

关键词： boundary value problem approximate solution subdivision algorithm collocation method refinable function

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The computational cost of clipping in parallel image processing

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Parallel algorithms and Applications 1995年第1-2期5卷 149-160页

作者： Christie, Ruth School of Computing Science Queensland University of Technology Brisbane Qld 4001 GPO Box 2434 Australia

When distributing the object data for rendering in a MIMD network all erroneous data must be clipped against each of the subdivisions of the image space which have been allocated to the individual processors. This process of clipping entails an added computational cost to that of the actual rendering algorithm. This paper looks at the effect of clipping on rendering in a parallel environment and determines a way of minimising the computational cost of that clipping when using a Transputer network. © 1995, Taylor & Francis Group, LLC. All rights reserved.

关键词： Clipping Hidden surface removal MIMD Parallel processing subdivision algorithm Transputer

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Real-Time Trajectory Generation for Mobile Robots in a Corridor-Like Space Using Bezier Curves

Real-Time Trajectory Generation for Mobile Robots in a Corri...

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IEEE/SICE International Symposium on System Integration (SII)

作者： Simba, Kenneth Renny Uchiyama, Naoki Sano, Shigenori Toyohashi Univ Technol Dept Mech Engn Tempaku Ku Toyohashi Aichi 4418580 Japan

ISBN: (纸本)9781479926268

This article deals with trajectory generation for teleoperated wheeled mobile robot using piecewise Bezier curves that are well-known to have useful properties. We develop an algorithm for generating motion trajectories with continuous curvature (C-2 continuity). We consider a teleoperated wheeled mobile robot in an indoor environment having ceiling cameras for operator's visibility. The motion trajectory is constrained by via points and path width designated by the operator. The Bezier subdivision method is employed and quintic Bezier segment is inserted in the high curvature area to improve the trackability by mobile robots. Simulation results demonstrate the feasibility of the proposed method.

关键词： mobile robot motion trajectory Bezier curve continuous curvature subdivision algorithm

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Grating Nanomeasurement and Implementation Technology Based on TMS320F28335

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International Conference on Frontiers of Manufacturing and Design Science (ICFMD2010)

作者： Xu, Congyu Hefei Univ Technol Sch Instrument Sci & Optoelect Engn Hefei 230009 Peoples R China

ISBN: (纸本)9783037850046

A grating nanomeasurement device based on TMS320F28335 was presented, a novel subdivision algorithm for nanomeasurement was put forward and implemented in TMS320F28335. The analysis and test show that, through the pre-amplifying circuit well designed and through the data process algorithm optimized, the device applied with 20 mu m pitch grating can realize +/-2nm resolution and greater than 200mm/s measurement speed. The experimental results of nanopositioning also demonstrate that the grating nanomeasurement device developed by the paper can be taken as nanomeasurement equipment used in nano-CMM and nanopositioning system.

关键词： TMS320F28335 Grating subdivision algorithm Nanomeasurement

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Computation of Compactly Supported Biorthogonal Riesz Basis of Wavelets 1

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1st International Conference on Computational Intelligence in Data Mining (ICCIDM)

作者： Jena, Mahendra Kumar Mishra, Manas Ranjan Veer Surendra Sai Univ Technol Dept Math Sambalpur 768018 Odisha India OP Jindal Inst Technol Dept Math Raigarh Chhattisgarh India

ISBN: (纸本)9788132222026;9788132222019

In this paper, we compute compactly supported biorthogonal Riesz basis of wavelets. We solve the Bezout equation resulting from biorthogonality of the scaling function with its dual in a simple and algebraic way. We provide some examples of the biorthogonal wavelets showing their detail construction. Two algorithms for their construction are also given.

关键词： Wavelet Biorthogonal subdivision algorithm

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Signal processing for single grating displacement measurement based on 3x3 coupler 9

Signal processing for single grating displacement measuremen...

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9th International Symposium on Precision Engineering Measurements and Instrumentation (ISPEMI)

作者： Wei, Chunhua Yan, Shuhua Lin, Cunbao Wang, Guochao Natl Univ Def Technol Coll Mechatron Engn & Automat Changsha 410073 Hunan Peoples R China

ISBN: (纸本)9781628415612

We present a compact displacement measurement system based on single grating and 3x3 coupler, possessing the capability of large range and nanometer precision. With the introduction of 3x3 coupler for phase shift in interference signal, the present scheme has the advantages of simple structure, convenient alignment, and insensitivity to air turbulence, resulting in high robustness. We accordingly developed an efficient and precision signal processing method for phase demodulation on a digital signal processing, adapting to characteristics of outputs in 3x3 coupler, achieving a high-powered subdivision of the interference phase. It was validated that the phase precision was about 1 degrees even when phase and amplitude errors were added to interference signals in the simulation, which corresponded to a displacement precision of about 3nm.

关键词： 3x3 coupler phase measurement fringe subdivision algorithm

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Clustering Complex Zeros of Triangular Systems of Polynomials

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MATHEMATICS IN COMPUTER SCIENCE 2021年第2期15卷 271-292页

作者： Imbach, Remi Pouget, Marc Yap, Chee NYU Courant Inst Math Sci 251 Mercer St New York NY 10012 USA Univ Lorraine CNRS INRIA LORIA F-54000 Nancy France

This paper gives the first algorithm for finding a set of natural epsilon-clusters of complex zeros of a regular triangular system of polynomials within a given polybox in (C)n, for any given epsilon > 0. Our algorithm is based on a recent near-optimal algorithm of Becker et al. (Proceedings of the ACM on international symposium on symbolic and algebraic computation, 2016) for clustering the complex roots of a univariate polynomial where the coefficients are represented by number oracles. Our algorithm is based on recursive subdivision. It is local, numeric, certified and handles solutions with multiplicity. Our implementation is compared to with well-known homotopy solvers on various triangular systems. Our solver always gives correct answers, is often faster than the homotopy solvers that often give correct answers, and sometimes faster than the ones that give sometimes correct results.

关键词： Complex root finding Triangular polynomial system Near-optimal root isolation Certified algorithm Complex root isolation Oracle multivariable polynomial subdivision algorithm Pellet's theorem

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Continued Fraction Expansion of Real Roots of Polynomial Systems

Continued Fraction Expansion of Real Roots of Polynomial Sys...

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International Workshop on Symbolic-Numeric Computation

作者： Mantzaflaris, Angelos Mourrain, Bernard Tsigaridas, Elias INRIA Sophia Antipolis GALAAD Sophia Antipolis France

ISBN: (纸本)9781605586649

We present a new algorithm for isolating the real roots of a system of multivariate polynomials, given in the monomial basis. It is inspired by existing subdivision methods in the Bernstein basis;it can be seen as generalization of the univariate continued fraction algorithm or alternatively as a fully analog of Bernstein subdivision in the monomial basis. The representation of the subdivided domains is done through homographies, which allows us to use only integer arithmetic and to treat efficiently unbounded regions. We use univariate bounding functions, projection and preconditionning techniques to reduce the domain of search. The resulting boxes have optimized rational coordinates, corresponding to the first terms of the continued fraction expansion of the real roots. An extension of Vincent's theorem to multivariate polynomials is proved and used for the termination of the algorithm. New complexity bounds are provided for a simplified version of the algorithm. Examples computed with a preliminary C++ implementation illustrate the approach.

关键词： subdivision algorithm homography tensor monomial basis continued fractions C plus plus implementation

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A Novel Precision Ultrasonic Thermometer

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International Conference on Mechatronics and Materials Processing (ICMMP 2011)

作者： Zhang, Xinghong Cai, Wei Xiang, Fengyun Zhang, Tianheng Liu, Shuxiang Chongqing Univ Technol Engn Res Ctr Mech Testing Technol & Equipment Minist Educ Chongqing Peoples R China

ISBN: (纸本)9783037852385

A new type of temperature measurement apparatus is designed by utilizing the characteristic that the velocity of the ultrasonic wave varies with the temperature through the medium, with both merits low cost and high precision. This paper introduces the principle of ultrasonic thermometer and puts forward the realization of hardware and software of thermometer, and details the special software subdivision algorithm which is used to measure the ultrasonic transmission time accurately. The experimental results indicate that the thermometer achieves the measure of the ultrasonic wave transmitting time with nanosecond level. The key problems are solved in the practical application of the ultrasonic temperature measuring technology, and the resolution of the temperature measurement is better than 0.001 centigrade.

关键词： Ultrasonic Thermometer subdivision algorithm Data Sampling FPGA

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Computing the Topology of Voronoi Diagrams of Parallel Half-Lines

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MATHEMATICS IN COMPUTER SCIENCE 2021年第4期15卷 859-876页

作者： Adamou, Ibrahim Mourrain, Bernard Univ Dan Dicko Dankoulodo Maradi Fac Sci & Tech Dept Math BP 465 Maradi Niger Univ Cote Azur INRIA 2004 Route LuciolesBP 93 F-06902 Sophia Antipolis France

In this paper we consider the Voronoi diagram of a finite family of parallel half-lines, with the same orientation, constrained to a compact domain D-0 subset of R-3, with respect to the Euclidean distance. We present an efficient approximation algorithm for computing such VD, using a subdivision process, which produces a mesh representing the topology of the VD in D-0. The computed topology may not be correct for degenerate configurations or configurations close to degenerate. In this case, the output is a valid partition, which is close to the exact partition in Voronoi cells if the input data were given with no error. We also present the result of an implementation in Julia language with visualization using Axl software (***) of the algorithm. Some examples and analysis are shown.

关键词： Voronoi diagram Parallel half-lines subdivision algorithm Kd-tree structure Algebraic curves and surfaces Topology

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