Stable Solution of Inverse Problems

I Basic Concepts.- 1 Introduction.- 2 Ill-posed problems.- 3 Regularization.- II Regularization Methods.- 4 The singular value decomposition.- 5 Applications of the singular value decomposition.- 6 The method of Tikhonov.- 7 Regularization by discretization.- III Least Squares Solutions of Systems of Linear Equations.- 8 Least squares problems.- 9 Numerical aspects of least squares problems.- IV Specific Topics.- 10 Convolution equations.- 11 The final value problem.- 12 Parameter identification.- References.- Notations.

I Basic Concepts. - 1 Introduction. - 2 Ill-posed problems. - 3 Regularization. - II Regularization Methods. - 4 The singular value decomposition. - 5 Applications of the singular value decomposition. - 6 The method of Tikhonov. - 7 Regularization by discretization. - III Least Squares Solutions of Systems of Linear Equations. - 8 Least squares problems. - 9 Numerical aspects of least squares problems. - IV Specific Topics. - 10 Convolution equations. - 11 The final value problem. - 12 Parameter identification. - References. - Notations.