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Sensitivity Analysis in Linear Systems

Author: Assem Deif
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1986.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:

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.

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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Assem Deif
ISBN: 9783642827396 364282739X
OCLC Number: 851373075
Description: 1 online resource (xii, 224 pages 17 illustrations)
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.
Responsibility: by Assem Deif.

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