عنوان

Sensitivity Analysis in Linear Systems

(Number (ISBN

364282739X

(Number (ISBN

9783642827396

Number

b574338

Title Proper

Sensitivity Analysis in Linear Systems

General Material Designation

[Book]

First Statement of Responsibility

by Assem Deif.

Place of Publication, Distribution, etc.

Berlin, Heidelberg

Name of Publisher, Distributor, etc.

Springer Berlin Heidelberg

Date of Publication, Distribution, etc.

1986

Specific Material Designation and Extent of Item

(xii, 224 pages 17 illustrations)

Text of Note

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.

Text of Note

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.

Computer engineering.

Engineering mathematics.

Engineering.

Class number

Book number

by Assem Deif.

Assem Deif

Electronic name

[Book]

Y