Inverse Problems:Tikhonov Theory and Algorithms (Series on by Kazufumi Ito,Bangti Jin

By Kazufumi Ito,Bangti Jin

Inverse difficulties come up in functional functions each time one must deduce unknowns from observables. This monograph is a precious contribution to the hugely topical box of computational inverse difficulties. either mathematical idea and numerical algorithms for model-based inverse difficulties are mentioned intimately. The mathematical conception specializes in nonsmooth Tikhonov regularization for linear and nonlinear inverse difficulties. The computational tools contain nonsmooth optimization algorithms, direct inversion tools and uncertainty quantification through Bayesian inference.

The ebook bargains a entire remedy of contemporary concepts, and seamlessly blends regularization concept with computational equipment, that is crucial for constructing exact and effective inversion algorithms for lots of sensible inverse problems.

It demonstrates many present advancements within the box of computational inversion, resembling worth functionality calculus, augmented Tikhonov regularization, multi-parameter Tikhonov regularization, semismooth Newton strategy, direct sampling procedure, uncertainty quantification and approximate Bayesian inference. it really is written for graduate scholars and researchers in arithmetic, average technology and engineering.

Contents:

  • Introduction
  • Models in Inverse Problems
  • Tikhonov conception for Linear Problems
  • Tikhonov concept for Nonlinear Inverse Problems
  • Nonsmooth Optimization
  • Direct Inversion Methods
  • Bayesian Inference

Readership: complex undergraduates, graduates and researchers in utilized arithmetic, computational arithmetic, optimization, facts, typical technology and engineering. it is going to entice these drawn to inverse problems.
Key Features:

  • A huge a part of the fabrics within the ebook is built through the authors, and so they haven't been taken care of in different books
  • A entire therapy of nonsmooth Tikhonov regularization, with a spotlight on worth functionality calculus, parameter selection principles, computational algorithms, and an optimization method of nonlinear inverse problems
  • A concise creation to quickly direct equipment for inverse difficulties, e.g., song set of rules, direct sampling approach, and Gel'fand–Levitan–Marchenko transformation
  • A special representation of uncertainty quantification for inverse difficulties through Bayesian inference, together with version choice, Markov chain Monte Carlo and approximate Bayesian inference

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