Titlebook: Stable Solution of Inverse Problems; Johann Baumeister Book 1987 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig 1987 Algebra.

壁画

Admonish

Applications of the singular value decompositionIn this chapter we demonstrate that the singular value decomposition of a compact operator plays a role in many different subjects. We restrict us to those topics which are related to problems in the next chapters.

简略

创造性

Regularization by discretizationHere we consider the discretization of ill-posed problems by projection methods. We present error estimates and convergence results.

Chameleon

Numerical aspects of least squares problemsThis chapter presents and analyses some problems which are related to the computation of least squares solutions. The aim is to make the reader familiar with the main tools and methods to calculate such solutions.

半导体

Convolution equationsIn this chapter we shall consider problems in which the Fourier transform plays an essential role: convolution equations, reconstruction from projections (see examples (E2), (E3) in Chapter 1).

incubus

The final value problemOne of the classical ill-posed problems (in the sense of Hadamard) is the final value problem for evolution equations; a special case of this problem is the solution of the heat equation backwards in time. We consider some regularization methods for this ill-posed problem.

REIGN

ParameteridentificationModels of systems in form of differential equations commonly contain parameters whose values are not fully known (see example (E5) in Chapter 1). In this chapter we consider some aspects of the identification of these model parameters from input-output data.

诽谤

Least squares problems. and ∥ ∥ denotes the euclidean distance. Our aim is to establish the mathematical material to discuss the computation of least squares solutions in the next chapter. The results are developed independently of results in Part II.

TEM