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Extended interval Newton method based on the precise quotient set

COMPUTING 2011年第4期92卷 297-315页

作者： Chen, Chin-Yun Natl Chiayi Univ Dept Appl Math Chiayi 600 Taiwan

The interval Newton method can be used for computing an enclosure of a single simple zero of a smooth function in an interval domain. It can practically be extended to allow computing enclosures of all zeros in a given interval. This paper deals with the extended interval Newton method. An essential operation of the method is division by an interval that contains zero (extended interval division). This operation has been studied by many researchers in recent decades, but inconsistency in the research has occurred again and again. This paper adopts the definition of extended interval division redefined in recent documents (Kulisch in Arithmetic operations for floating-point intervals, 2009;Pryce in P1788: IEEE standard for interval arithmetic version 02.2, 2010). The result of the division is called the precise quotient set. Earlier definitions differ in the overestimation of the quotient set in particular cases, causing inefficiency in Newton's method and even leading to redundant enclosures of a zero. The paper reviews and compares some extended interval quotient sets defined during the last few decades. As a central theorem, we present the fundamental properties of the extended interval Newton method based on the precise quotient set. On this basis, we develop an algorithm and a convenient program package for the extended interval Newton method. Statements on its convergence are also given. We then demonstrate the performance of the algorithm through nine carefully selected very sensitive numerical examples and show that it can compute correct enclosures of all zeros of the functions with high efficiency, particularly in cases where earlier methods are less effective.

关键词： Interval computation Extended interval division Newton method numerical algorithm

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OIL PRODUCTION, OIL PRICES, AND MACROECONOMIC ADJUSTMENT UNDER DIFFERENT WAGE ASSUMPTIONS

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INTERNATIONAL JOURNAL OF ENERGY RESEARCH 1992年第2期16卷 139-150页

作者： HARVIE, C MALEKA, PT 1Department of Economics University of Wollongong PO Box 1144 Northfields Avenue Wollongong NSW 2500 Australia2Rural Development Studies Bureau University of Zambia PO Box 32379 Lusaka Zambia

The paper is an extension to another paper recently published in this same journal by Harvie (1990a). In that paper he developed a simple model to try to identify the possible macroeconomic adjustment processes arising in an economy experiencing a temporary period of oil production, under alternative wage adjustment assumptions, namely nominal and real wage rigidity. Certain assumptions were made regarding the characteristics of actual oil production, the permanent revenues generated from that oil production, and the net exports/imports of oil. The role of the price of oil, and possible changes in that price, was essentially ignored, which was equivalent there to setting it to a value of zero. Hence Harvie (1990a) was effectively concerned with analysing the economic effects arising from the production of oil alone. Here we attempt to overcome this deficiency by incorporating the price of oil, as well as changes in that price, in conjunction with the production of oil, the objective being to identify the contribution which the price of oil, and changes in it, make to the adjustment process itself. As in Harvie (1990a), the emphasis in this paper is not given to a mathematical derivation and analysis of the model's dynamics of adjustment or its comparative statics. But rather to the derivation of simulation results from the model, for a specific assumed case, using a numerical algorithm program, conducive to the type of theoretical framework utilized here. The results presented suggest that although the adjustment profiles of the macroeconomic variables of interest, for either wage adjustment assumption, remain fundamentally the same, the magnitude of these adjustments is increased. Hence, to derive a more accurate picture of the dimensions of adjustment of these macroeconomic variables, it is essential to include the price of oil as well as changes in that price.

关键词： OIL PRICE CHANGES MACROECONOMIC FRAMEWORK numerical algorithm ADJUSTMENT PROFILE

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The validation of a semi-recursive vehicle dynamics model for a real-time simulation

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MECHANISM AND MACHINE THEORY 2020年 151卷 103907-103907页

作者： Pan, Yongjun Xiang, Saidi He, Yansong Zhao, Jian Mikkola, Aki Chongqing Univ Sch Automot Engn State Key Lab Mech Transmiss Chongqing 400044 Peoples R China Dalian Univ Technol Sch Automot Engn State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China Lappeenranta Univ Technol Dept Mech Engn Lappeenranta 53850 Finland

Semi-recursive formulations and their various versions have made it possible to describe complex nonlinear systems such as vehicles precisely while still solving the relevant equations of motion in real time. An optimal combination of an efficient multibody formulation and a fast numerical time integration scheme are needed to accurately simulate complex systems in real time. This paper introduces a double-step semi-recursive multibody formulation and analyzes its performance with high-order numerical time-integration algorithms for real-time simulation. The Runge-Kutta, Gill, Runge-Kutta-Fehlberg, Adams-Bashforth-Moulton, and adaptive time step Runge-Kutta numerical methods are explained and compared. Results are verified against a commercial multibody software solution. A 15-degree-of-freedom sedan vehicle model serves as a benchmark to verify the theoretical results. The results highlight the differences between the numerical algorithms and suggest appropriate approaches for a nonlinear vehicle dynamics model, particularly for cases where simulation times are long. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Real-time simulation Semi-recursive formulation numerical algorithm Vehicle dynamics Benchmark problem

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Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme

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JOURNAL OF COMPUTATIONAL PHYSICS 2004年第1期194卷 57-77页

作者： Yabe, T Mizoe, H Takizawa, K Moriki, H Im, HN Ogata, Y Tokyo Inst Technol Dept Mech Engn & Sci Meguro Ku Tokyo 1528552 Japan Tohoku Elect Power Co Inc Aoba Ku Sendai Miyagi 9810952 Japan

A new class of body-fitted grid system that can keep the third-order accuracy in time and space is proposed with the help of the CIP (constrained interpolation profile/cubic interpolated propagation) method. The grid system consists of the straight lines and grid points moving along these lines like abacus - Soroban in Japanese. The length of each line and the number of grid points in each line can be different. The CIP scheme is suitable to this mesh system and the calculation of large CFL (>10) at locally refined mesh is easily performed. Mesh generation and searching of upstream departure point are very simple and almost mesh-free treatment is possible. Adaptive grid movement and local mesh refinement are demonstrated. (C) 2003 Elsevier B.V. All rights reserved.

关键词： third-order scheme numerical algorithm curvilinear coordinate mesh free semi-Lagrangian schemes

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A stress point algorithm for an elastoplastic model in unsaturated soils

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INTERNATIONAL JOURNAL OF PLASTICITY 2000年第2期16卷 121-141页

作者： Vaunat, J Cante, JC Ledesma, A Gens, A Tech Univ Catalonia UPC Barcelona Spain

Two stress fields, combination of total stresses, liquid pressure and gas pressure have to be considered to explain the deformational behaviour of unsaturated media. Elastoplastic models developed for. these materials consider generally two yield surfaces, each one associated to a stress field, and whose intersection produces a corner in the space of generalised stress components. In this paper, a stress point algorithm is proposed to cope with the integration of such constitutive laws, which can be seen as non smooth multisurface plastic models in the space of the two stress fields. The basic model developed by Alonso et al. (Alonso, E.E., Gens, A., 1990. A constitutive model for partially saturated soils. Geotechnique 40 (3), 405-430), which will be used to test the algorithm, is first described. Generalised stress and strain variables are then defined. Implementation of the return mapping algorithm, based on an implicit integration scheme, is presented with special attention devoted to the problem of mixed control imposed by the F.E. formulation generally used to analyse the hydromechanical behaviour of unsaturated media. Validation results on distinct generalised stress paths are given at the end. (C) 2000 Published by Elsevier Science Ltd. All rights reserved.

关键词： plastic collapse geological material finite elements numerical algorithm unsaturated soils

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An efficient and versatile algorithm for computing the covariance function of an ARMA process

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 1998年第6期46卷 1591-1600页

作者： Soderstrom, T Jezek, J Kucera, V Uppsala Univ Dept Technol Syst & Control Grp Uppsala Sweden Acad Sci Czech Republ Inst Informat Theory & Automat CR-18208 Prague Czech Republic

Computation of an ARMA covariance function is a common ingredient in analysis and synthesis of various problems in stochastic control, estimation, and signal processing, Several approaches can be used for this purpose. In this paper, we present an algorithm based on simple polynomial calculations. Compared with alternative strategies, it has small computational load, shows good numerical robustness, and can be extended to handle multivariable ARMA processes, even with complex-valued coefficients.

关键词： ARMA process covariance function numerical algorithm numerical robustness polynomial algorithm

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Forced nonstationary vibrations of a sandwich cylindrical shell with cross-ribbed core

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INTERNATIONAL APPLIED MECHANICS 2005年第2期41卷 161-167页

作者： Lugovoi, PZ Meish, VF Shtantsel, SÉ Natl Acad Sci Ukraine SP Timoshenko Inst Mech Kiev Ukraine

The equations of nonaxisymmetric vibrations of sandwich cylindrical shells with discrete core under nonstationary loading are presented. The components of the elastic structure are analyzed using a refined Timoshenko theory of shells and rods. The numerical method used to solve the dynamic equations is based on the integro-interpolation method of constructing finite-difference schemes for equations with discontinuous coefficients. The dynamic problem for a sandwich cylindrical shell under distributed nonstationary loading is solved with regard for the discreteness of the core.

关键词： three-layer cylindrical shell ribbed core nonstationary loading Timoshenko theory numerical algorithm forced vibrations

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Solving system of Volterra-Fredholm integral equations with Bernstein polynomials and hybrid Bernstein Block-Pulse functions

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2017年 315卷 182-194页

作者： Hesameddini, Esmail Shahbazi, Mehdi Shiraz Univ Technol Dept Math Sci POB 71555-313 Shiraz Iran

This work approximates the unknown functions based on the Bernstein polynomials and hybrid Bernstein Block-Pulse functions, in conjunction with the collocation method for the numerical solution of system of Fredholm-Volterra integral equations. In both methods, the system of integral equations is approximated by the Gauss quadrature formula with respect to the Legendre weight function. The proposed methods reduce the system of integral equations to a system of algebraic equations that can be easily solved by any usual numerical methods. Moreover, the convergence analysis of these algorithms will be shown by preparing some theorems. numerical experiments are presented to show the superiority and efficiency of proposed methods in comparison with some other well known methods. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Bernstein polynomials System of Volterra-Fredholm integral equations Convergence analysis numerical algorithm Gaussian quadrature

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Space-Time Decomposition of Kalman Filter

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numerical Mathematics(Theory,Methods and Applications) 2023年第4期16卷 847-882页

作者： Luisa D’Amore Rosalba Cacciapuoti University of Naples Federico II NaplesItaly

We present an innovative interpretation of Kalman filter(KF)combining the ideas of Schwarz domain decomposition(DD)and parallel in time(PinT)*** we call it *** contrast to standard DD approaches which are already incorporated in KF and other state estimation models,implementing a straightforward data parallelism inside the loop over time,DD-KF ab-initio partitions the whole model,including filter equations and dynamic model along both space and time directions/*** a consequence,we get local KFs reproducing the original filter at smaller dimensions on local ***,sub problems could be solved in *** order to enforce the matching of local solutions on overlapping regions,and then to achieve the same global solution of KF,local KFs are slightly modified by adding a correction term keeping track of contributions of adjacent subdomains to overlapping *** a correction term balances localization errors along overlapping regions,acting as a regularization constraint on local ***,such a localization excludes remote observations from each analyzed location improving the conditioning of the error covariance *** dynamic model we consider shallow water equations which can be regarded a consistent tool to get a proof of concept of the reliability assessment of DD-KF in monitoring and forecasting of weather systems and ocean currents.

关键词： Data assimilation Kalman filter domain decomposition filter localization model reduction numerical algorithm

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Encoder based online motion planning and feedback control of redundant manipulators

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CONTROL ENGINEERING PRACTICE 2013年第10期21卷 1277-1289页

作者： Zhang, Yunong Li, Weibing Yu, Xiaotian Wu, Huarong Li, Jun Sun Yat Sen Univ Sch Informat Sci & Technol Guangzhou 510006 Guangdong Peoples R China Sun Yat Sen Univ Res Inst Shenzhen 518057 Peoples R China

This paper proposes and investigates an online motion planning and feedback control (OMPFC) scheme for redundant manipulators via techniques of quadratic programming and rotary encoder. The proposed OMPFC scheme is performed on a planar six degrees-of-freedom (DOF) manipulator. This robotic scheme incorporates the feedback of task-space position error. The joint state is obtained in real time via rotary encoders equipped on the physical manipulator. The original scheme is finally reformulated as a unified quadratic program (QP). The QP is solved online during the joint motion by employing an efficient numerical algorithm. Simulation and experimental results validate the physical realizability, online property, and efficacy of the proposed OMPFC scheme (including the employed numerical algorithm). (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Online motion planning and control Rotary encoder feedback numerical algorithm Global linear convergence Redundancy resolution

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