Groetsch, Charles W.
Stable Approximate Evaluation of Unbounded Operators [electronic resource] / by Charles W. Groetsch. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2007. - X, 133 p. online resource. - Lecture Notes in Mathematics, 1894 0075-8434 ; . - Lecture Notes in Mathematics, 1894 .
Some Problems Leading to Unbounded Operators -- Hilbert Space Background -- A General Approach to Stabilization -- The Tikhonov-Morozov Method -- Finite-Dimensional Approximations.
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.
9783540399438
10.1007/3-540-39942-9 doi
Mathematics.
Operator theory.
Numerical analysis.
Mathematics.
Operator Theory.
Numerical Analysis.
QA329-329.9
515.724
Stable Approximate Evaluation of Unbounded Operators [electronic resource] / by Charles W. Groetsch. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2007. - X, 133 p. online resource. - Lecture Notes in Mathematics, 1894 0075-8434 ; . - Lecture Notes in Mathematics, 1894 .
Some Problems Leading to Unbounded Operators -- Hilbert Space Background -- A General Approach to Stabilization -- The Tikhonov-Morozov Method -- Finite-Dimensional Approximations.
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.
9783540399438
10.1007/3-540-39942-9 doi
Mathematics.
Operator theory.
Numerical analysis.
Mathematics.
Operator Theory.
Numerical Analysis.
QA329-329.9
515.724