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Structure-Preserving Doubling Algorithms for Nonlinear Matrix Equations

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$59.00
Order Code:
FA14

 Product Description

by Tsung-Ming Huang, Ren-Cang Li, Wen-Wei Lin

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2018 / xii + 144 pages / Softcover / 978-1-611975-35-2 / List $59.00 / SIAM Member $41.30 / Order Code: FA14

Keywords: nonlinear matrix equation, algebraic Riccati equation, eigenvalue problem, doubling algorithm, entruwise accuracy

Contents
List of Figures;
List of Algorithms;
Preface;
Chapter 1: Introduction;
Chapter 2: Preliminaries;
Chapter 3: General Theory of Doubling Algorithms;
Chapter 4: Discrete-Time Algebraic Riccati Equation;
Chapter 5: Continuous-Time Algebraic Riccati Equation;
Chapter 6: M-matrix Algebraic Riccati Equation;
Chapter 7: Other Algebraic Riccati Equations;
Chapter 8: Nonlinear Matric Equations X + BX-1A = Q;
Bibliography;
Index.

Nonlinear matrix equations arise frequently in applied science and engineering. This is the first book to provide a unified treatment of structure-preserving doubling algorithms, which have been recently studied and proven effective for notoriously challenging problems, such as fluid queue theory and vibration analysis for high-speed trains. The authors present recent developments and results for the theory of doubling algorithms for nonlinear matrix equations associated with regular matrix pencils, and highlight the use of these algorithms in achieving robust solutions for notoriously challenging problems that other methods cannot.

Audience
Structure-Preserving Doubling Algorithms for Nonlinear Matrix Equations is intended for researchers and computational scientists. Graduate students may also find it of interest.

About the Authors
Tsung-Ming Huang is a professor in the department of mathematics at National Taiwan Normal University in Taipei, Taiwan. His research interests include large sparse linear systems, eigenvalue problems, and matrix equations.

Ren-Cang Li is a professor in the department of mathematics at University of Texas at Arlington. His research interests include floating-point support for scientific computing, large and sparse linear systems, eigenvalue problems, and model reduction, machine learning, and unconventional schemes for differential equations.

Wen-Wei Lin is a life-time chair professor in the department of applied mathematics at National Chiao Tung University in Taiwan. His research interests include numerical analysis, matrix computation in linear systems, eigenvalue problems, optimal controls, large-scale optimization in data science, chaotic dynamical systems, and computational conformal geometry with applications.

 

ISBN 9781611975352

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