Most applications of singular perturbation theory to control problems use a "zero order solution" as an approximation to an exact solution. Better approximations have traditionally been obtained by including...
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Most applications of singular perturbation theory to control problems use a "zero order solution" as an approximation to an exact solution. Better approximations have traditionally been obtained by including first and higher order terms. This paper considers a continuation method which deforms a "zero order solution" into an exact solution.
This revised and updated fourth edition designed for upper division courses in linearalgebra includes the basic results on vector spaces over fields, determinants, the theory of a single linear transformation, and in...
ISBN:
(纸本)9780387909929
This revised and updated fourth edition designed for upper division courses in linearalgebra includes the basic results on vector spaces over fields, determinants, the theory of a single linear transformation, and inner product spaces. While it does not presuppose an earlier course, many connections between linearalgebra and calculus are worked into the discussion. A special feature is the inclusion of sections devoted to applications of linearalgebra, which can either be part of a course, or used for independent study, and new to this edition is a section on analytic methods in matrix theory, with applications to Markov chains in probability theory. Proofs of all the main theorems are included, and are presented on an equal footing with methods for solving numerical problems. Worked examples are integrated into almost every section, to bring out the meaning of the theorems, and illustrate techniques for solving problems. Many numerical exercises make use of all the ideas, and develop computational skills, while exercises of a theoretical nature provide opportunities for students to discover for themselves.
We present a unifying framework for a wide class of iterative methods in numericallinearalgebra. In particular, the class of algorithms contains Kaczmarz's and Richardson's methods for the regularized weight...
We present a unifying framework for a wide class of iterative methods in numericallinearalgebra. In particular, the class of algorithms contains Kaczmarz's and Richardson's methods for the regularized weighted least squares problem with weighted norm. The convergence theory for this class of algorithms yields as corollaries the usual convergence conditions for Kaczmarz's and Richardson's methods. The algorithms in the class may be characterized as being group-iterative, and incorporate relaxation matrices, as opposed to a single relaxation parameter. We show that some well-known iterative methods of image reconstruction fall into the class of algorithms under consideration, and are thus covered by the convergence theory. We also describe a novel application to truly three-dimensional image reconstruction.
This paper focuses on the interplay between recent results and methodologies in numericallinearalgebra and mathematical software and their application to problems arising in systems, control, and estimation theory. ...
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This paper focuses on the interplay between recent results and methodologies in numericallinearalgebra and mathematical software and their application to problems arising in systems, control, and estimation theory. Some key results in numericallinearalgebra are surveyed and a guide to the literature is provided. A number of issues in mathematical software are then outlined. Finally, a selected list of applications of the previous subjects to problems in systems, control, and estimation is discussed.
This paper focuses on the interplay between problems arising in linear control and systems theory and their solution by recent results and methodologies in numericallinearalgebra. The following are among the topics ...
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This paper focuses on the interplay between problems arising in linear control and systems theory and their solution by recent results and methodologies in numericallinearalgebra. The following are among the topics addressed: numerical calculation of various objects arising in the geometric theory of multivariable control; special matrix equations such as Lyapunov, Sylvester, and Riccati equations; controllability; and efficient frequency response calculations. applications of some of the topics are mentioned and embodiment of the theory and algorithms as reliable mathematical software is also discussed. The format is kept expository and many open problems are featured throughout.
A simple numerical procedure is presented for the inversion of a system S(A, B, C) satisfying the constraints CAi−1B=0, 1 ≤ i ≤ k – 1, and CAk−1B ¬ 0 for some k ≥ 1. The results generalise the work of Kouvari...
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A simple numerical procedure is presented for the inversion of a system S(A, B, C) satisfying the constraints CAi−1B=0, 1 ≤ i ≤ k – 1, and CAk−1B ¬ 0 for some k ≥ 1. The results generalise the work of Kouvaritakis for the case of k = 1.
This paper focuses on the interplay between problems arising in linear control and systems theory and their solution by recent results and methodologies in numericallinearalgebra. The following are among the topics ...
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This paper focuses on the interplay between problems arising in linear control and systems theory and their solution by recent results and methodologies in numericallinearalgebra. The following are among the topics addressed: numerical calculation of various objects arising in the geometric theory of multivariable control;special matrix equations such as Lyapunov, Sylvester, and Riccati equations;controllability;and efficient frequency response calculations. applications of some of the topics are mentioned and embodiment of the theory and algorithms as reliable mathematical software is also discussed. The format is kept expository and many open problems are featured throughout.
D A H Jacobs (ed) London: Academic 1977 pp xix + 978 price £20 This book contains the papers given at a conference organised by the Institute of Mathematics and its applications and held at York in April 1976. Th...
D A H Jacobs (ed) London: Academic 1977 pp xix + 978 price £20 This book contains the papers given at a conference organised by the Institute of Mathematics and its applications and held at York in April 1976. The conference aim was to survey the major research areas in numerical analysis, and the book contains sections on: numericallinearalgebra; error analysis; optimisation; ordinary differential equations and quadrature; approximation theory; partial differential equations; and integral equations.
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