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Spectral theory of bounded linear operators teams up with von Neumann’s theory of unbounded operators in this monograph to provide a general framework for the study of stable methods for the evaluation of unbounded operators. An introductory chapter provides numerous illustrations of unbounded linear operators that arise in various inverse problems of mathematical physics. Before the general theory of stabilization methods is developed, an extensive exposition of the necessary background material from the theory of operators on Hilbert space is provided. Several specific stabilization methods are studied in detail, with particular attention to the Tikhonov-Morozov method and its iterated version.

Operatortheorie. --- Numerieke methoden. --- Linear operators. --- Inverse problems (Differential equations) --- Operator theory. --- Approximation theory. --- Opérateurs linéaires --- Problèmes inversés (Equations différentielles) --- Théorie des opérateurs --- Théorie de l'approximation --- Algebras, Linear. --- Electronic books. -- local. --- Linear operators --- Operator theory --- Approximation theory --- Mathematical Theory --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Linear algebra --- Linear maps --- Maps, Linear --- Operators, Linear --- Mathematics. --- Numerical analysis. --- Operator Theory. --- Numerical Analysis. --- Mathematical analysis --- Functional analysis --- Math --- Science --- Algebra, Universal --- Generalized spaces --- Calculus of operations --- Line geometry --- Topology --- Problèmes inversés (Équations différentielles) --- Opérateurs, Théorie des. --- Opérateurs linéaires. --- Approximation, Théorie de l'. --- Differential equations --- Theory of approximation --- Functions --- Polynomials --- Chebyshev systems