Hardcover ISBN:  9780883851418 
Product Code:  CAR/32 
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AMS Member Price:  $56.25 
eBook ISBN:  9781614440291 
Product Code:  CAR/32.E 
List Price:  $70.00 
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AMS Member Price:  $52.50 
Hardcover ISBN:  9780883851418 
eBook: ISBN:  9781614440291 
Product Code:  CAR/32.B 
List Price:  $145.00 $110.00 
MAA Member Price:  $108.75 $82.50 
AMS Member Price:  $108.75 $82.50 
Hardcover ISBN:  9780883851418 
Product Code:  CAR/32 
List Price:  $75.00 
MAA Member Price:  $56.25 
AMS Member Price:  $56.25 
eBook ISBN:  9781614440291 
Product Code:  CAR/32.E 
List Price:  $70.00 
MAA Member Price:  $52.50 
AMS Member Price:  $52.50 
Hardcover ISBN:  9780883851418 
eBook ISBN:  9781614440291 
Product Code:  CAR/32.B 
List Price:  $145.00 $110.00 
MAA Member Price:  $108.75 $82.50 
AMS Member Price:  $108.75 $82.50 

Book DetailsThe Carus Mathematical MonographsVolume: 32; 2016; 320 pp
Inverse problems occur frequently in science and technology, whenever we need to infer causes from effects that we can measure. Mathematically, they are difficult problems because they are unstable: small bits of noise in the measurement can completely throw off the solution. Nevertheless, there are methods for finding good approximate solutions.
Linear Inverse Problems and Tikhonov Regularization examines one such method: Tikhonov regularization for linear inverse problems defined on Hilbert spaces. This is a clear example of the power of applying deep mathematical theory to solve practical problems. Beginning with a basic analysis of Tikhonov regularization, this book introduces the singular value expansion for compact operators, and uses it to explain why and how the method works. Tikhonov regularization with seminorms is also analyzed, which requires introducing densely defined unbounded operators and their basic properties. Some of the relevant background is included in appendices, making the book accessible to a wide range of readers.

Table of Contents

Chapters

Chapter 1. Introduction to inverse problems

Chapter 2. Wellposed, illposed, and inverse problems

Chapter 3. Tikhonov regularization

Chapter 4. Compact operators and the singular value expansion

Chapter 5. Tikhonov regularization with seminorms


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Inverse problems occur frequently in science and technology, whenever we need to infer causes from effects that we can measure. Mathematically, they are difficult problems because they are unstable: small bits of noise in the measurement can completely throw off the solution. Nevertheless, there are methods for finding good approximate solutions.
Linear Inverse Problems and Tikhonov Regularization examines one such method: Tikhonov regularization for linear inverse problems defined on Hilbert spaces. This is a clear example of the power of applying deep mathematical theory to solve practical problems. Beginning with a basic analysis of Tikhonov regularization, this book introduces the singular value expansion for compact operators, and uses it to explain why and how the method works. Tikhonov regularization with seminorms is also analyzed, which requires introducing densely defined unbounded operators and their basic properties. Some of the relevant background is included in appendices, making the book accessible to a wide range of readers.

Chapters

Chapter 1. Introduction to inverse problems

Chapter 2. Wellposed, illposed, and inverse problems

Chapter 3. Tikhonov regularization

Chapter 4. Compact operators and the singular value expansion

Chapter 5. Tikhonov regularization with seminorms