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IEEE conference on Decision and Control

作者： W.W. Hager Department of Mathematics University of Florida Gainesville FL USA

For pt.I see J. Optim. theory Appl., vol.55, p.37-71 (1987). An algorithm for constrained optimization that combines an unconstrained minimization scheme like the conjugate gradient method, an augmented Lagrangian, and multiplier updates to obtain global quadratic convergence was presented in part I. Issues related to the numerical implementation of the algorithm are considered here. The convergence theory is extended to handle the rigid constraints that are not violated during the iterations. A strategy is developed for balancing the error associated with constraint violation with the error associated with optimality. Various numerical linear algebra techniques required for the efficient implementation of the algorithm are also developed, and the convergence properties of the algorithm are illustrated using some standard test problems.< >

关键词： Constraint optimization Lagrangian functions Gradient methods Convergence Upper bound Mathematics Minimization methods Constraint theory linear algebra Standards development

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linear-SYSTEM REDUCTION USING APPROXIMATE MOMENT MATCHING

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IEE PROCEEDINGS-D CONTROL theory AND applications 1988年第2期135卷 73-78页

作者： DAVIDSON, AM WALTERS, IR Department of Mathematics University of Wales Institute of Science and Technology Cardiff UK

A method for reduction of continuous-time linear systems is presented which employs a singular-value decomposition approximation to Hankel matrices. The method is related both to balancing reduction and to moment-matc... 详细信息

关键词： Control system analysis and synthesis methods Simulation, modelling and identification balancing reduction linear systems continuous time systems control system analysis approximate moment matching algebra matrix algebra Interpolation and function approximation (numerical analysis) singular-wave decomposition approximation model reduction approximation theory Hankel matrices modelling

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International symposium on Trends in Computer algebra, 1987

International symposium on Trends in Computer Algebra, 1987

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International symposium on Trends in Computer algebra, 1987

ISBN: (纸本)9783540189282

The proceedings contain 13 papers. The special focus in this conference is on Trends in Computer algebra. The topics include: Application of scratchpad to problems in special functions and combinatorics;Programming with abstract data types: The symmetry package SPDE in scratchpad;algebraic computation, numerical computation and verified inclusions;intelligent computer algebra system: Myth, fancy or reality?;Scratchpad II: An abstract datatype system for mathematical computation;current trends in rewriting techniques and related problems;applications of Gröbner bases in non-linear computational geometry;factorisation of polynomials: Old ideas and recent results;generalized fourier transforms;representations of groups over finite fields;computational methods in constructive Galois theory.

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NEW TABLE TO IMPLEMENT ROUTH STABILITY TEST AND MATRIX CONTINUED-FRACTION EXPANSION AND INVERSION

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IEE PROCEEDINGS-D CONTROL theory AND applications 1987年第5期134卷 327-332页

作者： THERAPOS, CP Department of Electrical Engineering National Technical University of Athens Athens Greece

A new table of numbers, obtained by rearranging the well known Routh stability array, is used to perform Routh's stability test. The proposed table, with slight modifications, can also be used to expand a known rational transfer function matrix into one of the three Cauer-form continued fractions, or, conversely, to invert a given Cauer-form continued fraction. In all the aforementioned applications, the recursive relations presented for the construction of the proposed table seem better than the relevant Routh-type relations, as one may follow more easily the values of the indices appearing in the formulas, while the number of the variables involved is significantly decreased. Moreover, from the programming point of view, they guarantee a reduction of the required memory, nearly by half, and a faster execution of the corresponding program. These advantages are achieved without increase of the number of numerical operations or in the complexity of the existing techniques.

关键词： matrix continued fraction expansion Routh stability array Cauer-form continued fractions Routh's stability test inversion polynomials matrix algebra linear algebra (numerical analysis) convergence of numerical methods rational transfer function matrix

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SHIFTED LEGENDRE APPROACH TO THE ANALYSIS AND IDENTIFICATION OF A linear DELAYED SYSTEM WITH A NONlinear GAIN

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IEE PROCEEDINGS-D CONTROL theory AND applications 1986年第3期133卷 127-132页

作者： SHIH, DH KUNG, FC Department of Electrical Engineering National Cheng Kung University Tainan Republic of China

applications of the shifted Legendre polynomials expansion to the analysis and identification of the nonlinear time-delayed system, described by a memoryless nonlinear element followed by a linear plant with time delay, are studied. The system described here is assumed both controllable and observable. For analysis, by using the shifted Legendre polynomials expansion, the solution of a nonlinear state equation is reduced to the solution of a linear algebraic matrix equation. For identification, through the shifted Legendre expansions of the measured input/output data, the unknown parameters of both the linear delayed plant and the characterisation of the nonlinear element are estimated by using the least-squares method. Algorithms are presented. numerical examples are given to illustrate the use of this approach.

关键词： nonlinear gain Nonlinear control systems linear algebraic matrix equation Simulation, modelling and identification nonlinear systems control system analysis least-squares method nonlinear state equation matrix algebra shifted Legendre polynomials expansion Distributed parameter control systems delays Control system analysis and synthesis methods identification linear delayed system

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PLASTIC FLOW OF VOID CONTAINING METALS - applications TO AXISYMMETRIC SHEET FORMING PROBLEMS.

PLASTIC FLOW OF VOID CONTAINING METALS - APPLICATIONS TO AXI...

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Proceedings of the 2nd International conference on numerical methods in Industrial Forming Processes: NUMIFORM 86.

作者： Onate, E. Kleiber, M. Univ Politecnica Cataluna Spain Univ Politecnica Cataluna Spain

ISBN: (纸本)9061916593

A formal analogy between the equations of pure plastic flow theory for void containing metals and those of standard elasticity is presented. The formulation is particularized for the analysis of axisymmetric sheet metal forming problems using simple two node linear finite elements. Examples of the effect of void porosity on the hemispherical stretching of a circular sheet are presented.

关键词： SHEET AND STRIP METAL

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numerical linear algebra ASPECTS OF CONTROL DESIGN COMPUTATIONS

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1985年第2期30卷 97-108页

作者： LAUB, AJ Department of Electrical and Computer Engineering University of California Santa Barbara CA USA

The interplay between recent results and methodologies in numerical linear algebra and mathematical software and their application to problems arising in systems, control, and estimation theory is discussed. The impact of finite precision, finite range arithmetic [including the implications of the proposed IEEE floating point standard(s)] on control design computations is illustrated with numerous examples as are pertinent remarks concerning numerical stability and conditioning. Basic tools from numerical linear algebra such as linear equations, linear least squares, eigenproblems, generalized eigenproblems, and singular value decomposition are then outlined. A selected list of applications of the basic tools then follows including algorithms for solution of problems such as matrix exponentials, frequency response, system balancing, and matrix Riccati equations. The implementation of such algorithms as robust mathematical software is then discussed. A number of issues are addressed including characteristics of reliable mathematical software, availability and evaluation, language implications (Fortran, Ada, etc.), and the overall role of mathematical software as a component of computer-aided control system design.

关键词： linear algebra Control design Riccati equations Application software Control systems Matrix decomposition Estimation theory Floating-point arithmetic numerical stability Least squares methods

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Nearness Problems in numerical linear algebra

Nearness Problems in Numerical Linear Algebra

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作者： Higham, Nicholas J. The University of Manchester

学位级别：博士

We consider the theoretical and the computational aspects of some nearness problems in numerical linear algebra. Given a matrix A, a matrix norm and a matrix property P, we wish to find the distance from A to the class of matrices having property P, and to compute a nearest matrix from this class. It is well-known that nearness to singularity is measured by the reciprocal of the matrix condition number. We survey and compare a wide variety of techniques for estimating the condition number and make recommendations concerning the use of the estimates in applications. We express the solution to the nearness to unitary and nearness to Hermitian positive (semi-) definiteness problems in terms of the polar decomposition. A quadratically convergent Newton iteration for computing the unitary polar factor is presented and analysed, and the iteration is developed into a practical algorithm for computing the polar decomposition. applications of the algorithm to factor analysis, aerospace computations and optimisation are described; and the algorithm is used to derive a new method for computing the square root of a symmetric positive definite matrix. This leads us, in the remainder of the thesis, to consider the theory and computation of matrix square roots. We analyse the convergence properties and the numerical stability of several well-known Newton methods for computing the matrix square root. By means of a perturbation analysis and supportive numerical examples it is shown that two of these Newton iterations are numerically unstable. The polar decomposition algorithm, and a further Newton square root iteration are shown not to suffer from this numerical instability. For a nonsingular real matrix A we derive conditions for the existence of a real square root, and for the existence of a real square root which is a polynomial in A; the number of square roots of the latter type is determined. We show how a Schur method recently proposed by Bjorck and Hammarling can be extended

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numerical SOLUTION OF NON-linear PARABOLIC EQUATIONS ON PARALLEL COMPUTERS BY GROUP EXPLICIT methods.

NUMERICAL SOLUTION OF NON-LINEAR PARABOLIC EQUATIONS ON PARA...

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NUMETA 85, numerical methods in Engineering: theory and applications, Proceedings of the International conference.

作者： Evans, D.J. Loughborough Univ of Technology Loughborough Engl Loughborough Univ of Technology Loughborough Engl

ISBN: (纸本)9061915775

This paper investigates the applicability of a new class of group explicit methods for the numerical solution of a non-linear parabolic partial differential equation to parallel processing. The method is briefly presented and then concentrates on the specific implementation details for the DAP and CRAY parallel computers. A numerical example is given and some impressive results on the speed-ups in favour of the parallel architecture are given. (Edited author abstract. ) Refs.

关键词： MATHEMATICAL TECHNIQUES

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numerical methods IN LIMIT ANALYSIS FOR ANISOTROPIC MATERIALS.

NUMERICAL METHODS IN LIMIT ANALYSIS FOR ANISOTROPIC MATERIAL...

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NUMETA 85, numerical methods in Engineering: theory and applications, Proceedings of the International conference.

作者： Turgeman, S. Pastor, J. Boehler, J.P. Inst de Mecanique de Grenoble Grenoble Fr Inst de Mecanique de Grenoble Grenoble Fr

ISBN: (纸本)9061915775

A numerical approach for the determination of the limit loads of mechanical systems composed of anisotropic materials is proposed. Materials considered are those obeying the Von Mises and Tresca criteria generalized for transverse isotropic media within the theory of the plastic behavior of anisotropic solids proposed by J. P. Boehler. The developed numerical programs are based on the static and kinematic methods of Limit Analysis. After discretization of the medium in finite elements and linearization of the yield criteria, these methods lead to problems of linear optimization, which are solved by computer codes. Several applications are presented. (Edited author abstract. )

关键词： MATERIALS SCIENCE

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