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Linear Inverse Problems and Tikhonov Regularization by Mark Gockenbach (Michigan Technological University) at Abbey's Bookshop,
Linear Inverse Problems and Tikhonov Regularization
— —
Mark Gockenbach (Michigan Technological University)

Linear Inverse Problems and Tikhonov Regularization

Mark Gockenbach (Michigan Technological University)

$92.95

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English
Mathematical Association of America
24 November 2016
Numerical analysis; Linear programming
Series: Carus Mathematical Monographs
Tikhonov regularization is the most popular general-purpose method for regularization, a mathematical technique to suppress the effect of noise in data, and uses much of the machinery of Hilbert space theory. This book develops the theory of Tikhonov regularization for a certain class of linear inverse problems which are defined on Hilbert spaces. To explain why and how Tikhonov regularization works, the singular value expansion for compact operators is introduced. Tikhonov regularization with seminorms is also analyzed and for this purpose, densely defined unbounded operators are addressed and their basic properties presented. In addition, the author provides readers with a quick but thorough review of Hilbert space theory and a brief introduction to weak derivatives and Sobolev spaces. Intended as an expository work for those interested in inverse problems and Tikhonov regularization, including graduates and researchers, the author presents the theory in an engaging and straightforward style.
By:  
Imprint:   Mathematical Association of America
Country of Publication:   United States
Volume:   32
Dimensions:   Height: 216mm,  Width: 146mm,  Spine: 23mm
Weight:   470g
ISBN:   9780883851418
ISBN 10:   0883851415
Series:   Carus Mathematical Monographs
Pages:   336
Publication Date:  
Audience:   College/higher education ,  Primary
Format:   Hardback
Publisher's Status:   Active
Preface; 1. Introduction to inverse problems; 2. Well-posed, ill-posed, and inverse problems; 3. Tikhonov regularization; 4. Compact operators and the singular value expansion; 5. Tikhonov regularization with seminorms; Epilogue; A. Basic Hilbert space theory; B. Sobolev spaces; Bibliography; Index.

Mark Gockenbach received his Ph.D. in Computational and Applied Mathematics from Rice University, Houston and has since held faculty positions at Indiana University, the University of Michigan and Rice University. He is now Professor and Chair of the Department of Mathematical Sciences at Michigan Technological University and has won several awards for teaching. He also serves as a volunteer lecturer in the International Mathematical Union's Volunteer Lecturer Program (VLP) where he has taught master's degree courses in Phnom Penh, Cambodia. He has published several books on inverse problems in partial differential equations, including Partial Differential Equations: Analytical and Numerical Methods (first edition 2002, second edition 2010) and Understanding and Implementing the Finite Element Method (2006).

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