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numerical algorithms for polynomial plus/minus factorization

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2007年第8期17卷 786-802页

作者： Hromcik, M. Sebek, M. Czech Tech Univ Fac Elect Engn Ctr Appl Cybernet CR-16635 Prague Czech Republic Czech Tech Univ Fac Elect Engn Dept Control Engn CR-16635 Prague Czech Republic

Two new algorithms are presented in the paper for the plus/minus factorization of a scalar discrete-time polynomial. The first method is based on the discrete Fourier transform theory (DFT) and its relationship to the Z-transform. Involving DFT computational techniques and the famous fast Fourier transform routine brings high computational efficiency and reliability. The method is applied in the case study of H-2-optimal inverse dynamic filter to an audio equipment. The second numerical procedure originates in a symmetric spectral factorization routine, namely the Bauer's method of the 1950s. As a by-product, a recursive LU factorization procedure for Toeplitz matrices is devised that is of more general impact and can be of use in other areas of applied mathematics as well. Performance of the method is demonstrated by an l(1) optimal controller design example. Copyright (c) 2006 John Wiley & Sons, Ltd.

关键词： polynomial design methods numerical algorithms polynomial factorizations

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numerical algorithms for approximation of fractional integral operators based on quadratic interpolation

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2018年第9期41卷 3345-3355页

作者： Blaszczyk, Tomasz Siedlecki, Jaroslaw Ciesielski, Mariusz Czestochowa Tech Univ Inst Math Al Armii Krajowej 21 PL-42200 Czestochowa Poland Czestochowa Tech Univ Inst Comp & Informat Sci Dabrowskiego 73 PL-42200 Czestochowa Poland

We present numerical algorithms calculating compositions of the left and right fractional integrals. We apply quadratic interpolation and obtain the fractional Simpson's rule. We estimate the local truncation error of the proposed approximations, calculate errors generated by presented algorithms, and determine the experimental rate of convergence. Finally, we show examples of numerical evaluation of these operators.

关键词： fractional integrals numerical algorithms quadratic interpolation Simpson's rule

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numerical algorithms for spatial registration of line fiducials from cross-sectional images

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MEDICAL PHYSICS 2002年第8期29卷 1881-1891页

作者： Lee, S Fichtinger, G Chirikjian, GS Johns Hopkins Univ Dept Mech Engn Baltimore MD 21218 USA Johns Hopkins Univ Ctr Comp Integrated Surg Syst & Technol Baltimore MD 21218 USA

We present several numerical algorithms for six-degree-of-freedom rigid-body registration of line fiducial objects to their marks in cross-sectional planar images, such as those obtained in CT and MRI, given the correspondence between the marks and line fiducials. The area of immediate application is frame-based stereotactic procedures, such as radiosurgery and functional neurosurgery. The algorithms are also suitable to problems where the fiducial pattern moves inside the imager, as is the case in robot-assisted image-guided surgical applications. We demonstrate the numerical methods on clinical CT images and computer-generated data and compare their performance in terms of robustness to missing data, robustness to noise, and speed. The methods show two unique strengths: (1) They provide reliable registration of incomplete fiducial patterns when up to two-thirds of the total fiducials are missing from the image;and (2) they are applicable to an arbitrary combination of line fiducials without algorithmic modification. The average speed of the fastest algorithm is 0.3236 s for six fiducial lines in real CT data in a Matlab implementation. (C) 2002 American Association of Physicists in Medicine.

关键词： stereotactic registration line fiducials numerical algorithms robustness

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numerical algorithms for Identification of Convection Coefficient and Source in a Magnetohydrodynamics Flow

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algorithms 2024年第9期17卷 387页

作者： Kandilarov, Juri D. Vulkov, Lubin G. Univ Ruse Dept Math 8 Studentska Str Ruse 7017 Bulgaria

We consider three integral observations inverse problems (IP1, IP2, IP3) for reconstruction of a time-dependent convection coefficient and a source in magnetohydrodynamics (MHD) model. On the first stage, using the integral observations, we reduce the inverse problems to nonclassical direct (forward) ones. The equivalence between the inverse and direct problems is established. Then, the well-posedness of nonclassical problems is proved. Further, to overcome the difficulties arising from the nonlinear nonlocal parabolic operators, we construct a linarization algorithm in time after their difference space discretizatons. Next, on each iteration, to solve the corresponding linear systems of algebraic equations, we propose adequate fast elimination algorithms. Computational results of test examples data are discussed.

关键词： magnetohydrodynamics inverse problem numerical algorithms

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numerical algorithms and issues concerning the discrete-time optimal projection equations

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EUROPEAN JOURNAL OF CONTROL 2000年第1期6卷 93-110页

作者： Van Willigenburg, LG De Koning, WL Univ Wageningen & Res Ctr Syst & Control Grp Agrotechnion NL-6703 HD Wageningen Netherlands Delft Univ Technol Fac Math & Informat NL-2628 CD Delft Netherlands

The discrete-time optimal projection equations, which constitute necessary conditions fir optimal reduced-order LQG compensation, are strengthened. For the class of minimal stabilizing compensators the strengthened discrete-time optimal projection equations are proved to he equivalent to first-order necessary optimality conditions for optimal reduced-order LQG compensation. The conventional discrete-time optimal projection equations are pro red to be weaker. As a result solutions of the conventional discrete-time optimal projection equations may not correspond to optimal reduced-order compensators. Through numerical examples it is demonstrated that, in fact, many solutions exist that do not correspond to optimal reduced-order compensators. To compute optimal reduced-order compensators two licit, algorithms are proposed. One is a homotopy algorithm and one is based oil iteration of the strengthened discrete-time optimal projection equations. The latter algorithm is a generalization of the algorithm that solves the two Riccati equations of full-order LQG control through iteration and therefore is highly efficient. Using different initializations of the iterative algorithm it is demonstrated that the reduced-order optimal LQG compensation problem, in general, may possess multiple extrema. Through two computer experiments it is demonstrated that the homotopy algorithm often, but not always, finds the global minimum.

关键词： optimal reduced-order dynamic compensation fixed-order LQG control discrete-time systems numerical algorithms

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numerical algorithms for Systems with Extramassive Parallelism

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2020年第5期60卷 783-794页

作者： Osipova, V. P. Chetverushkin, B. N. Russian Acad Sci Fed Res Ctr Keldysh Inst Appl Math Moscow 125047 Russia

Difficulties associated with ultrahigh-performance computer systems that will appear in the near future and possible ways of their solution are discussed. Examples of simulating magnetogasdynamics problems are given.

关键词： high-performance computations extramassive parallelism numerical algorithms quasi-gasdynamic system of equations magnetogasdynamics

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numerical algorithms for Lyapunov Stability Analysis of Interpolative Control Structures 6

Numerical Algorithms for Lyapunov Stability Analysis of Inte...

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6th International Conference on Computers Communications and Control (ICCCC)

作者： Dale, Sanda Zmaranda, Doina Silaghi, Helga Gabor, Gianina Univ Oradea Dept Automat & Appl Informat Oradea Romania Univ Oradea Dept Comp Sci & IT Oradea Romania

ISBN: (纸本)9781509017355

The complexity and specificity of stability analysis applied to interpolative-type control structures makes the study of such property a difficult, almost impossible task - at least in the analytical manner. Therefore, a better solution could be represented by the numerical approach. In this context, this paper starts with developing some methods and techniques with applicability for analysis of the interpolative-type controllers, based on Lyapunov method perspective. These methodological aspects are gathered together into a specific procedural algorithm. Based on this algorithm, a set of MATLAB-SIMULINK programs able to offer, in a flexible and user-interactive way, a possible solution to Lyapunov-stability analysis for a class of interpolative-type control systems with linear or non-linear processes of 2nd and 3rd order are developed. The solution based on the implemented software packages was finally validated through some practical examples.

关键词： numerical algorithms Lyapunov-stability analysis interpolative controllers Shepard interpolation

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numerical algorithms and issues concerning the discrete-time optimal projection equations for systems with white parameters

Numerical algorithms and issues concerning the discrete-time...

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UKACC International Conference on Control 98

作者： De Koning, WL Van Willigenburg, LG Delft Univ Technol Fac Tech Math & Informat NL-2628 CD Delft Netherlands

ISBN: (纸本)085296708X

The discrete-time optimal projection equations for systems with white parameters are strengthened. For the class of minimal ms (mean square) stabilizing compensators the strengthened discrete-time optimal projection equations are proved to be equivalent to first-order necessary optimality conditions for optimal reduced-order dynamic compensation of systems with white parameters. The conventional discrete-time optimal projection equations are proved to be weaker. As a result solutions of the conventional discrete-time optimal projection equations may not correspond to optimal reduced-order compensators. To compute optimal reduced-order compensators two numerical algorithms are proposed. One is a homotopy algorithm and one is based on iteration of the strengthened discrete-time optimal projection equations. The latter algorithm is a generalization of the algorithm that solves the full-order problem, which in turn is a generalization of the algorithm that solves the two Riccati equations of full-order LQG control through iteration. Therefore the efficiency of these three types of algorithms is comparable. It is demonstrated that, despite the strengthening of the optimal projection equations, the optimal reduced-order compensation problem, in general, may posses multiple extrema.

关键词： multiplicative white noise white stochastic parameters reduced-order control numerical algorithms optimal projection equations

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A unified approach for the convergence of certain numerical algorithms, using recurrent functions

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COMPUTING 2010年第3-4期90卷 131-164页

作者： Argyros, Ioannis K. Hilout, Said Cameron Univ Dept Math Sci Lawton OK 73505 USA Univ Poitiers Lab Math & Applicat F-86962 Futuroscope France

The Kantorovich analysis (Argyros in Convergence and applications of Newton-type iterations, Springer, New York, 2008;Argyros and Hi lout in Efficient methods for solving equations and variational inequalities, Polimetrica Publisher, Milano, 2009;Kantorovich and Akilov in Functional analysis, Pergamon Press, Oxford, 1982), and recurrent relation's approach (Gutierrez et al. in J Comput Appl Math 115:181-192,2000) are the most popular ways for generating sufficient conditions for the convergence of numerical algorithms to a solution of a nonlinear equations as well as providing the corresponding error estimates on the distances involved. We introduce the new approach of recurrent functions to show that a finer convergence analysis can be provided under the same hypotheses, and computational cost. numerical examples are provided where our results apply, hut not earlier ones.

关键词： numerical algorithms Banach space Majorizing sequence Newton-Kantorovich hypothesis Semilocal convergence Recurrent functions Boundary value problem with a Green's kernel

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An Automated Framework for Accelerating numerical algorithms on Reconfigurable Platforms Using Algorithmic/Architectural Optimization

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IEEE TRANSACTIONS ON COMPUTERS 2009年第12期58卷 1654-1667页

作者： Kim, Jung Sub Deng, Lanping Mangalagiri, Prasanth Irick, Kevin Sobti, Kanwaldeep Kandemir, Mahmut Narayanan, Vijaykrishnan Chakrabarti, Chaitali Pitsianis, Nikos Sun, Xiaobai Penn State Univ Dept Comp Sci & Engn University Pk PA 16802 USA Arizona State Univ Dept Elect Engn Tempe AZ 85287 USA Duke Univ Dept Comp Sci Durham NC 27708 USA

This paper describes TANOR, an automated framework for designing hardware accelerators for numerical computation on reconfigurable platforms. Applications utilizing numerical algorithms on large-size data sets require high-throughput computation platforms. The focus is on N-body interaction problems which have a wide range of applications spanning from astrophysics to molecular dynamics. The TANOR design flow starts with a MATLAB description of a particular interaction function, its parameters, and certain architectural constraints specified through a graphical user interface. Subsequently, TANOR automatically generates a configuration bitstream for a target FPGA along with associated drivers and control software necessary to direct the application from a host PC. Architectural exploration is facilitated through support for fully custom fixed-point and floating-point representations in addition to standard number representations such as single-precision floating point. Moreover, TANOR enables joint exploration of algorithmic and architectural variations in realizing efficient hardware accelerators. TANOR's capabilities have been demonstrated for three different N-body interaction applications: the calculation of gravitational potential in astrophysics, the diffusion or convolution with Gaussian kernel common in image processing applications, and the force calculation with vector-valued kernel function in molecular dynamics simulation. Experimental results show that TANOR-generated hardware accelerators achieve lower resource utilization without compromising numerical accuracy, in comparison to other existing custom accelerators.

关键词： algorithms implemented in hardware reconfigurable hardware signal processing systems numerical algorithms

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