Sensitivity Analysis in Linear Systems
Springer Berlin (Verlag)
978-3-642-82741-9 (ISBN)
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.
Erscheint lt. Verlag | 8.12.2011 |
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Zusatzinfo | XII, 224 p. |
Verlagsort | Berlin |
Sprache | englisch |
Maße | 170 x 244 mm |
Gewicht | 421 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
Technik ► Elektrotechnik / Energietechnik | |
Schlagworte | Calculus • Circuit • Design • linear optimization • Modeling • Network • Numerical analysis • programming • Regression |
ISBN-10 | 3-642-82741-1 / 3642827411 |
ISBN-13 | 978-3-642-82741-9 / 9783642827419 |
Zustand | Neuware |
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