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Mathematical Sciences --- Applied Mathematics --- Complex Analysis --- General and Others --- Mathematics --- Fonctions d'une variable complexe --- Functions of complex variables --- Functions of complex variables. --- Periodicals.

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Functions of complex variables --- Mathematical analysis --- Differential equations, Elliptic --- Fonctions d'une variable complexe --- Analyse mathématique --- Differential equations, Elliptic. --- Functions of complex variables. --- Mathematical analysis. --- Advanced calculus --- Analysis (Mathematics) --- Complex variables --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- 517.1 Mathematical analysis --- Algebra --- Elliptic functions --- Functions of real variables --- Differential equations, Linear --- Differential equations, Partial --- Calculus --- Équations différentielles elliptiques

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Mathematical analysis --- Mathematics --- Physical sciences --- Functions of complex variables. --- Mathematical analysis. --- Advanced calculus --- Analysis (Mathematics) --- Algebra --- Complex variables --- Elliptic functions --- Functions of real variables --- Science --- 517.1 Mathematical analysis --- Mathematics. --- Math

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Geometric function theory --- Fonctions, Théorie géométrique des --- Geometric function theory. --- Function theory, Geometric --- Functions of complex variables --- Théorie géométrique des fonctions --- Funktionentheorie --- Komplexe Analysis --- Komplexe Funktionentheorie --- Analysis --- Komplexe Funktion

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Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods. This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels.

Banach spaces --- Parameter estimation --- Differential equations, Partial --- Banach, Espaces de --- Estimation d'un paramètre --- Equations aux dérivées partielles --- Banach spaces. --- Parameter estimation. --- Differential equations, Partial. --- Partial differential equations --- Estimation theory --- Stochastic systems --- Functions of complex variables --- Generalized spaces --- Topology --- Banach Space. --- Iterative Method. --- Regularization Theory. --- Tikhonov Regularization.