Overview

A text surveying perturbation techniques and sensitivity analysis of linear systems is an ambitious undertaking, considering the lack of basic comprehensive texts on the subject. A wide-ranging and global coverage of the topic is as yet missing, despite the existence of numerous monographs dealing with specific topics but generally of use to only a narrow category of people. In fact, most works approach this subject from the numerical analysis point of view. Indeed, researchers in this field have been most concerned with this topic, although engineers and scholars in all fields may find it equally interesting. One can state, without great exaggeration, that a great deal of engineering work is devoted to testing systems' sensitivity to changes in design parameters. As a rule, high-sensitivity elements are those which should be designed with utmost care. On the other hand, as the mathematical modelling serving for the design process is usually idealized and often inaccurately formulated, some unforeseen alterations may cause the system to behave in a slightly different manner. Sensitivity analysis can help the engineer innovate ways to minimize such system discrepancy, since it starts from the assumption of such a discrepancy between the ideal and the actual system.

Full Product Details

Author:   Assem Deif
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 1986
Dimensions:   Width: 17.00cm , Height: 1.20cm , Length: 24.40cm
Weight:   0.422kg
ISBN:  

9783642827419

ISBN 10:   3642827411
Pages:   224
Publication Date:   08 December 2011
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

1 Perturbation of Linear Equations.- 1.1 Introduction.- 1.2 Norms of Vectors and Matrices.- 1.3 Condition Number and Nearness to Singularity.- 1.4 A-priori Bounds.- 1.5 Pivoting and Equilibration.- 1.6 Sensitivity Analysis: A Circuit Theory Interpretation.- 1.7 An Application on Error Bounds: Lyapunov’s Equation.- 2 Methods of Interval Analysis.- 2.1 Introduction.- 2.2 Interval Arithmetic.- 2.3 Hansen’s Methods.- 2.4 Method of Linear Programming.- 2.5 A-posteriori Bounds.- 2.6 Two Problems in Interval Analysis.- 2.7 An Application to Electrical Networks.- 3 Iterative Systems.- 3.1 Introduction.- 3.2 An Alternative Bound.- 3.3 Rates of Convergence.- 3.4 Accuracy of Solutions.- 3.5 A Method for Order Reduction.- 3.6 Methods of Iterative Refinement.- 3.7 Case of Interval Coefficients.- 4 The Least-Squares Problem.- 4.1 Introduction.- 4.2 Perturbations of the Moore-Penrose Inverse.- 4.3 Accuracy of Computation.- 4.4 Case of Interval Coefficients.- 4.5 Least-Squares in Regression.- 5 Sensitivity in Linear Programming.- 5.1 Introduction.- 5.2 Parametric Programming and Sensitivity Analysis.- 5.3 The Problem of Ranging in Linear Programming.- 5.4 Interval Programming.- 5.5 Programming Under Uncertainty.- 5.6 Distributions of Solution.- References.

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