We present a theory for reduced-order modelling of linear time-varying systems, together with efficient numericalmethods for application to large systems. The technique, called TVP (Time-Varying Pade), is applicable ...
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ISBN:
(纸本)1581130082
We present a theory for reduced-order modelling of linear time-varying systems, together with efficient numericalmethods for application to large systems. The technique, called TVP (Time-Varying Pade), is applicable to deterministic as well as noise analysis of many types of communication subsystems, such as mixers and switched-capacitor filters, for which existing model reduction techniques cannot be used. TVP is therefore suitable for hierarchical verification of entire communication systems. We present practical applications in which TVP generates macromodels which are more than two orders of magnitude smaller, but still replicate the input-output behaviour of the original systems accurately. The size reduction results in a speedup of more than 500.
The numerical Algorithms Group Ltd is currently participating in the European HPCN Fourth Framework project on Parallel industrial Aum-Erical applications and Portable Libraries (PINEAPL). One of the main goals of the...
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ISBN:
(纸本)3540649522
The numerical Algorithms Group Ltd is currently participating in the European HPCN Fourth Framework project on Parallel industrial Aum-Erical applications and Portable Libraries (PINEAPL). One of the main goals of the project is to increase the suitability of the existing NAG Parallel Library for dealing with computationally intensive industrial applications by appropriately extending the range of library routines. Additionally, several industrial applications are being ported onto parallel computers within the PINEAPL project by replacing sequential code sections with calls to appropriate parallel library routines. A substantial part of the library material being developed is concerned with the solution of PDE problems using parallel sparse linearalgebra modules. This talk provides a number of performance results which demonstrate the efficiency and scalability of core computational routines - in particular, the iterative solver, the preconditioner and the matrix-vector multiplication routines. Most of the software described in this talk has been incorporated into the recently launched Release 1 of the PINEAPL Library.
An extensive revision of the author's highly successful text, this third edition of linear System theory and Design has been made more accessible to students from all related backgrounds. After introducing the fun...
ISBN:
(纸本)9780195117776
An extensive revision of the author's highly successful text, this third edition of linear System theory and Design has been made more accessible to students from all related backgrounds. After introducing the fundamental properties of linear systems, the text discusses design using state equations and transfer functions. In state-space design, Lyapunov equations are used extensively to design state feedback and state estimators. In the discussion of transfer-function design, pole placement, model matching, and their applications in tracking and disturbance rejection are covered. Both one-and two-degree-of-freedom configurations are used. All designs can be accomplished by solving sets of linearalgebraic equations. The two main objectives of the text are to: DT use simple and efficient methods to develop results and design procedures DT enable students to employ the results to carry out design All results in this new edition are developed for numerical computation and illustrated using MATLAB, with an emphasis on the ideas behind the computation and interpretation of results. This book develops all theorems and results in a logical way so that readers can gain an intuitive understanding of the theorems. This revised edition begins with the time-invariant case and extends through the time-varying case. It also starts with single-input single-output design and extends to multi-input multi-output design. Striking a balance between theory and applications, linear System theory and Design, 3/e, is ideal for use in advanced undergraduate/first-year graduate courses in linear systems and multivariable system design in electrical, mechanical, chemical, and aeronautical engineering departments. It assumes a working knowledge of linearalgebra and the Laplace transform and an elementary knowledge of differential equations.
The use of polynomial matrices and equations in linear systems and signals is surveyed and recent progress is reported that has namely be achieved in numerical algorithms. The new generation routines for polynomial ma...
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The use of polynomial matrices and equations in linear systems and signals is surveyed and recent progress is reported that has namely be achieved in numerical algorithms. The new generation routines for polynomial matrices are both faster and more reliable. They make industrial applications of the polynomial methods possible in the fields of control and signal processing. Based on the new algorithms, a new software package - Polynomial Toolbox for Matlab Version 2.0 - has been developed that is powerful, object oriented and user-friendly.
The use of polynomial matrices and equations in linear systems and signals is surveyed and progress is reported that has mainly been achieved in numerical algorithms. The new generation routines for polynomial matrice...
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The use of polynomial matrices and equations in linear systems and signals is surveyed and progress is reported that has mainly been achieved in numerical algorithms. The new generation routines for polynomial matrices are both faster and more reliable. They make industrial applications of the polynomial methods possible in the fields of control and signal processing. Based on the new algorithms, a new software package-Polynomial Toolbox for Matlab Version 2.0-has been developed that is powerful, object oriented and user-friendly.
Chebechev's inequality theorem from the theory of probability and statistics provides an upper bound for the amount of probability in the "tails" of any given probability density function. This theorem h...
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Chebechev's inequality theorem from the theory of probability and statistics provides an upper bound for the amount of probability in the "tails" of any given probability density function. This theorem has interesting applications in the numerical solution of the Fokker-Planck-Kolmogorov equation (FPKE) as shown in this paper. numerical solution of FPKE is an essential component of the design of optimal nonlinear filters. The solution of the FPKE in conjunction with the Bayes' conditional density lemma provides optimal (minimum variance) state estimates of any general stochastic dynamic system (SDS).
We present a theory for reduced order modelling of linear time varying systems, together with efficient numericalmethods for application to large systems. The technique, called TVP (Time-Varying Pade), is applicable ...
详细信息
We present a theory for reduced order modelling of linear time varying systems, together with efficient numericalmethods for application to large systems. The technique, called TVP (Time-Varying Pade), is applicable to deterministic as well as noise analysis of many types of communication subsystems, such as mixers and switched capacitor filters, for which existing model reduction techniques cannot be used. TVP is therefore suitable for hierarchical verification of entire communication systems. We present practical applications in which TVP generates macromodels which are more than two orders of magnitude smaller but still replicate the input-output behaviour of the original systems accurately. The size reduction results in a speedup of more than 500.
In an earlier paper we exploited the displacement structure of Cauchy-like matrices to derive for them a fast O(n(2)) implementation of Gaussian elimination with partial pivoting. One application is to the rapid and n...
In an earlier paper we exploited the displacement structure of Cauchy-like matrices to derive for them a fast O(n(2)) implementation of Gaussian elimination with partial pivoting. One application is to the rapid and numerically accurate solution of linear systems with Toeplitz-like coefficient matrices, based on the fact that the latter can be transformed into Cauchy-like matrices by using the fast Fourier, sine, or cosine transform. However, symmetry is lost in the process, and the algorithm given is not optimal for Hermitian coefficient matrices. In this paper we present a new fast O(n(2)) implementation of symmetric Gaussian elimination with partial diagonal pivoting for Hermitian Cauchy-like matrices, and show how to transform Hermitian Toeplitz-like matrices to Hermitian Cauchy-like matrices, obtaining algorithms that are twice as fast as those in the earlier work. numerical experiments indicate that in order to obtain not only fast but also numerically accurate methods, it is advantageous to explore the important case in which the corresponding displacement operators have nontrivial kernels;this situation gives rise to what we call partially reconstructible matrices, which are introduced and studied in the present paper. We extend the transformation technique and the generalized Schur algorithms (i.e., fast displacement-based imple mentations of Gaussian elimination) to partially reconstructible matrices. We show by a variety of computed examples that the incorporation of diagonal pivoting methods leads to high accuracy. We focused in this paper on the design of new numerically reliable algorithms for Hermitian Toeplitz-like matrices. How ever, the proposed algorithms have other important applications;in particular, we briefly describe how they recursively solve a boundary interpolation problem for J-unitary rational matrix functions.
The proceedings contain 71 papers. The special focus in this conference is on numerical Analysis and Its applications. The topics include: The Newtonian continuation method for numerical study of 3D polaron problem;pa...
ISBN:
(纸本)3540625984
The proceedings contain 71 papers. The special focus in this conference is on numerical Analysis and Its applications. The topics include: The Newtonian continuation method for numerical study of 3D polaron problem;parallel iterative solvers for banded linear systems;finite element approximations of some central curves;numerical algorithm for simulation of coupled heat-mass transfer and chemical reaction in two-phase steady flow;basic techniques for numericallinearalgebra on bulk synchronous parallel computers;convergence of a crank-Nicolson difference scheme for heat equations with interface in the heat flow and concentrated heat capacity;boundary value methods for the numerical approximation of ordinary differential equations;splitting time methods and one dimensional special meshes for reaction-diffusion parabolic problems;the use of discrete sine transform in computations with toeplitz matrices;a finite state stochastic minimax optimal control problem with infinite horizon;operator problems in strengthened sobolev spaces and numericalmethods for them;convex combinations of matrices-nonsingularity and schur stability;componentwise error bounds and direct linear system solving;a method for solving the spectral problem for complex matrices;interpolation technique and convergence rate estimates for finite difference method;least squares and total least squares methods in image restoration;numericalmethods for computation of the double layer logarithmic potential;numerical analysis in singularly perturbed boundary value problems modelling heat transfer processes;improved perturbation bounds for the matrix exponential and spectral portrait of matrices by block diagonalization.
We present, in matrix notation, general Bartlett correction formulae for several hypotheses in generalized linear models with dispersion covariates. These results generalize previous work by Cordeiro (1983, 1993) who ...
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We present, in matrix notation, general Bartlett correction formulae for several hypotheses in generalized linear models with dispersion covariates. These results generalize previous work by Cordeiro (1983, 1993) who obtained Bartlett corrections for generalized linear models with known dispersion parameter and for multiplicative heteroscedastic normal models, respectively. The formulae derived are simple enough to be used analytically to obtain several closed form Bartlett corrections in a variety of important tests when the information. matrix has a closed form. They also have advantages for numerical purposes since our formulae are readily computable using a language supporting numericallinearalgebra. We give applications to some special models and discuss improved likelihood ratio tests.
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