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.
Ideal for graduates and researchers, this book covers the theory of Tikhonov regularization for linear inverse problems defined on Hilbert spaces.
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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