The book collects and contributes new results on the theory and practice of ill-posed inverse problems. Different notions of ill-posedness in Banach spaces for linear and nonlinear inverse problems are discussed not only in standard settings but also in situations up to now not covered by the literature. Especially, ill-posedness of linear operators with uncomplemented null spaces is examined.Tools for convergence rate analysis of regularization methods are extended to a wider field of applicability. It is shown that the tool known as variational source condition always yields convergence rate results. A theory for nonlinear inverse problems with quadratic structure is developed as well as corresponding regularization methods. The new methods are applied to a difficult inverse problem from laser optics.Sparsity promoting regularization is examined in detail from a Banach space point of view. Extensive convergence analysis reveals new insights into the behavior of Tikhonov-type regularization with sparsity enforcing penalty.

The book collects and contributes new results on the theory and practice of ill-posed inverse problems. Different notions of ill-posedness in Banach spaces for linear and nonlinear inverse problems are discussed not only in standard settings but also in situations up to now not covered by the literature. Especially, ill-posedness of linear operators with uncomplemented null spaces is examined.Tools for convergence rate analysis of regularization methods are extended to a wider field of applicability. It is shown that the tool known as variational source condition always yields convergence rate results. A theory for nonlinear inverse problems with quadratic structure is developed as well as corresponding regularization methods. The new methods are applied to a difficult inverse problem from laser optics.Sparsity promoting regularization is examined in detail from a Banach space point of view. Extensive convergence analysis reveals new insights into the behavior of Tikhonov-type regularization with sparsity enforcing penalty.

Dieses Buch, eine Sammlung von Quellen, erzählt vom Ersten Weltkrieg. Sein Thema ist der Alltag im Ausnahmezustand, womit das Leben jenseits der Friedensjahre, jenseits auch der darin gültigen Normen, Werte und Sinnbezüge gemeint ist. In den Texten spiegeln sich die Erfahrungen von Frauen und Männern, Müttern und Vätern, Kindern und Jugendlichen, von Leuten unterschiedlichster Profession und Herkunft, von Versehrten und Hinterbliebenen. Berichtet wird von Hoffnungen und Illusionen ebenso wie von Enttäuschung und Not. Dabei werden Strategien sichtbar, mit denen man sich gegen die Zumutungen einer aus den Fugen geratenen Welt zu wappnen sucht. So wird das Außergewöhnliche alltäglich: in den Schützengräben und auf den Schlachtfeldern ebenso wie zu Hause in den Städten und Dörfern.

The book collects and contributes new results on the theory and practice of ill-posed inverse problems. Different notions of ill-posedness in Banach spaces for linear and nonlinear inverse problems are discussed not only in standard settings but also in situations up to now not covered by the literature. Especially, ill-posedness of linear operators with uncomplemented null spaces is examined.Tools for convergence rate analysis of regularization methods are extended to a wider field of applicability. It is shown that the tool known as variational source condition always yields convergence rate results. A theory for nonlinear inverse problems with quadratic structure is developed as well as corresponding regularization methods. The new methods are applied to a difficult inverse problem from laser optics.Sparsity promoting regularization is examined in detail from a Banach space point of view. Extensive convergence analysis reveals new insights into the behavior of Tikhonov-type regularization with sparsity enforcing penalty.

The book collects and contributes new results on the theory and practice of ill-posed inverse problems. Different notions of ill-posedness in Banach spaces for linear and nonlinear inverse problems are discussed not only in standard settings but also in situations up to now not covered by the literature. Especially, ill-posedness of linear operators with uncomplemented null spaces is examined.Tools for convergence rate analysis of regularization methods are extended to a wider field of applicability. It is shown that the tool known as variational source condition always yields convergence rate results. A theory for nonlinear inverse problems with quadratic structure is developed as well as corresponding regularization methods. The new methods are applied to a difficult inverse problem from laser optics.Sparsity promoting regularization is examined in detail from a Banach space point of view. Extensive convergence analysis reveals new insights into the behavior of Tikhonov-type regularization with sparsity enforcing penalty.

Dieses Buch, eine Sammlung von Quellen, erzählt vom Ersten Weltkrieg. Sein Thema ist der Alltag im Ausnahmezustand, womit das Leben jenseits der Friedensjahre, jenseits auch der darin gültigen Normen, Werte und Sinnbezüge gemeint ist. In den Texten spiegeln sich die Erfahrungen von Frauen und Männern, Müttern und Vätern, Kindern und Jugendlichen, von Leuten unterschiedlichster Profession und Herkunft, von Versehrten und Hinterbliebenen. Berichtet wird von Hoffnungen und Illusionen ebenso wie von Enttäuschung und Not. Dabei werden Strategien sichtbar, mit denen man sich gegen die Zumutungen einer aus den Fugen geratenen Welt zu wappnen sucht. So wird das Außergewöhnliche alltäglich: in den Schützengräben und auf den Schlachtfeldern ebenso wie zu Hause in den Städten und Dörfern.