Theory of Linear Ill-Posed Problems and its Applications

By V. Ivanov, V. Vasin, V. P. Tanana. 2002

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Inverse problems in spaces of measures (2013, background): “While the basic regularization theory of inverse problems is well-established in Hilbert spaces [22] and for linear problems in Banach spaces [34], recent interest focuses on specific linear and non-linear problems usually set in Banach spaces [4,9,21,31,32,38,43,44,49].”
Integral equations and applications (2015, methodology): “as a solution, this solution may diﬀer very much from the solution to equation (15). Such problems are called ill-posed. They are important in many applications, especially in inverse problems, [15], [4] . The usual statement of the problem of solving an ill-posed equation (15) consists of the follo”
Data Errors and an Error Estimation for Ill-Posed Problems (2002, methodology): “Let us consider the method of extending compacts [7,20].”
Simultaneous determination of source terms in a linear parabolic problem from the final overdetermination: Weak solution approach (2007, background): “of the inverse problem (1)–(2), according to [11,16], as a solution of the minimization problem for the cost functional J (w), given by (3): J (w∗) = inf w∈W J(w).”