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Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.

519.61 --- Numerical methods of algebra --- Differential equations, Partial --- Iterative methods (Mathematics) --- Improperly posed problems. --- Iterative methods (Mathematics). --- Differential equations, Partial -- Improperly posed problems. --- Mathematics. --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Improperly posed problems --- 519.61 Numerical methods of algebra --- Iteration (Mathematics) --- Improperly posed problems in partial differential equations --- Ill-posed problems --- Inkorrekt gestelltes Problem. --- Regularisierungsverfahren. --- Iteration. --- Nichtlineares inverses Problem. --- Numerical analysis --- Iterative Regularization. --- Nonlinear Ill-Posed Problems. --- Nonlinear Inverse Problems.

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Inverse problems such as imaging or parameter identification deal with the recovery of unknown quantities from indirect observations, connected via a model describing the underlying context. While traditionally inverse problems are formulated and investigated in a static setting, we observe a significant increase of interest in time-dependence in a growing number of important applications over the last few years. Here, time-dependence affects a) the unknown function to be recovered and / or b) the observed data and / or c) the underlying process. Challenging applications in the field of imaging and parameter identification are techniques such as photoacoustic tomography, elastography, dynamic computerized or emission tomography, dynamic magnetic resonance imaging, super-resolution in image sequences and videos, health monitoring of elastic structures, optical flow problems or magnetic particle imaging to name only a few. Such problems demand for innovation concerning their mathematical description and analysis as well as computational approaches for their solution.

Numerical analysis --- Mathematics --- Computer. Automation --- computervisie --- informatica --- wiskunde --- numerieke analyse

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This book is a collection of thoroughly refereed papers presented at the 26th IFIP TC 7 Conference on System Modeling and Optimization, held in Klagenfurt, Austria, in September 2013. The 34 revised papers were carefully selected from numerous submissions. They cover the latest progress in a wide range of topics such as optimal control of ordinary and partial differential equations, modeling and simulation, inverse problems, nonlinear, discrete, and stochastic optimization as well as industrial applications.

Computer science. --- Numerical analysis. --- Computer science --- Mathematical statistics. --- Mathematical optimization. --- Computer Science. --- Numeric Computing. --- Discrete Mathematics in Computer Science. --- Probability and Statistics in Computer Science. --- Optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Informatics --- Science --- Mathematics. --- Statistical methods --- Electronic data processing. --- Computational complexity. --- Complexity, Computational --- Machine theory --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Automation --- Control theory --- Computer science—Mathematics. --- Discrete mathematics. --- Numerical Analysis. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis

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Numerical analysis --- Mathematics --- Computer. Automation --- computervisie --- informatica --- wiskunde --- numerieke analyse

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Mathematics