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Viser: Discrete Inverse Problems - Insight and Algorithms
Discrete Inverse Problems
Insight and Algorithms
Per Christian Hansen
(2010)
Sprog: Engelsk
Society for Industrial and Applied Mathematics
1.217,00 kr.
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Detaljer om varen
- Paperback: 225 sider
- Udgiver: Society for Industrial and Applied Mathematics (Februar 2010)
- ISBN: 9780898716962
Inverse problems arise when we reconstruct a sharper image from a blurred one or reconstruct the underground mass density from measurements of the gravity above the ground. When we solve an inverse problem, we compute the source that gives rise to some observed data using a mathematical model for the relation between the source and the data.
This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.
Discrete Inverse Problems includes a number of tutorial exercises that give the reader hands-on experience with the methods, difficulties, and challenges associated with the treatment of inverse problems. It also includes examples and figures that illustrate the theory and algorithms.
This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.
Discrete Inverse Problems includes a number of tutorial exercises that give the reader hands-on experience with the methods, difficulties, and challenges associated with the treatment of inverse problems. It also includes examples and figures that illustrate the theory and algorithms.
Preface
List of Symbols
Chapter 1: Introduction
and Motivation
Chapter 2: Meet the Fredholm Integral Equation of the First Kind
Chapter 3: Getting to Business: Discretizations of Linear Inverse Problems
Chapter 4: Computational Aspects: Regularization Methods
Chapter 5: Getting Serious: Choosing the Regularization Parameter
Chapter 6: Toward Real-World Problems: Iterative Regularization
Chapter 7: Regularization Methods at Work: Solving Real Problems
Chapter 8: Beyond the 2-Norm: The Use of Discrete Smoothing Norms
Appendix A: Linear Algebra Stuff
Appendix B: Symmetric Toeplitz-Plus-Hankel Matrices and the DCT
Appendix C: Early Work on "Tikhonov Regularization" Bibliography
Index
List of Symbols
Chapter 1: Introduction
and Motivation
Chapter 2: Meet the Fredholm Integral Equation of the First Kind
Chapter 3: Getting to Business: Discretizations of Linear Inverse Problems
Chapter 4: Computational Aspects: Regularization Methods
Chapter 5: Getting Serious: Choosing the Regularization Parameter
Chapter 6: Toward Real-World Problems: Iterative Regularization
Chapter 7: Regularization Methods at Work: Solving Real Problems
Chapter 8: Beyond the 2-Norm: The Use of Discrete Smoothing Norms
Appendix A: Linear Algebra Stuff
Appendix B: Symmetric Toeplitz-Plus-Hankel Matrices and the DCT
Appendix C: Early Work on "Tikhonov Regularization" Bibliography
Index
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