New trends in parameter identification for mathematical models. (2018)

• Record Type: Book
• Further Information: Note: Bernd Hofmann, Antonio Leitão, Jorge P. Zubelli, editors.
• Editors: Hofmann, Bernd; Leitão, António; Zubelli, Jorge P
• Other Names: IMPA Conference "New Trends in Parameter Identification for Mathematical Models"
• Contents: Intro; Preface; Contents; Posterior Contraction in Bayesian Inverse Problems Under Gaussian Priors; 1 Setup; 1.1 Squared Posterior Contraction; 1.2 Paradigm; 1.3 Outline; 2 Setting the Pace; 3 Assumptions and Main Results; 3.1 Link Conditions, Source Sets and Qualification; 3.2 Bounding the Bias; 3.3 The Net Posterior Spread; 3.4 Main Result: Bounding the Squared Posterior Contraction; 4 Examples and Discussion; 4.1 Sobolev Smoothness; 4.1.1 Moderately Ill-Posed Operator; 4.1.2 Severely Ill-Posed Operator; 4.2 Analytic-Type Smoothness; 4.2.1 Moderately Ill-Posed Operator. 4.2.2 Severely Ill-Posed Operator4.3 Summary and Discussion; Appendix; References; Convex Regularization of Discrete-Valued Inverse Problems; 1 Introduction; 2 Multi-Bang Penalty; 3 Multi-Bang Regularization; 4 Pointwise Convergence; 5 Structure of Minimizers; 6 Numerical Solution; 7 Numerical Examples; 8 Conclusion; References; Algebraic Reconstruction of Source and Attenuation in SPECT Using First Scattering Measurements; 1 Introduction; 2 Model Description; 2.1 Integral Operators; 2.2 Ballistic and First Scattering Measurements; 3 Inverse Problem; 3.1 Albedo Operator. 3.2 Linearized Inverse Problem4 Reconstruction Algorithm; 4.1 Linear System and General Algorithm; 4.2 Discretization and Matrices Construction; 4.2.1 Matrix A0 Construction; 4.2.2 Matrix A1 Construction; 5 Numerical Experiments; References; On 1-Regularization Under Continuity of the Forward Operator in Weaker Topologies; 1 Introduction; 2 Preliminaries and Basic Propositions; 3 Ill-Posedness and Conditional Stability; 4 Convergence Rates Results for 1-Regularization; 5 Extensions to Non-reflexive Image Spaces; 6 The Well-Posed Case and Further Discussions; References. On Self-regularization of Ill-Posed Problems in Banach Spaces by Projection Methods1 Introduction; 2 The General Projection Method; 2.1 Convergence with A Priori Choice of n; 2.2 Convergence with A Posteriori Choice of n: The Discrepancy Principle; 3 The Least Squares Method; 4 Application: Collocation Method for Volterra Integral Equations; 4.1 Cordial Integral Equations; 4.2 Polynomial Collocation Method for Cordial Integral Equations, Numerical Results; 4.3 Spline-Collocation for Volterra Integral Equation, Numerical Results; References. Monotonicity-Based Regularization for Phantom Experiment Data in Electrical Impedance Tomography1 Introduction; 2 Mathematical Setting; 3 Monotonicity-Based Regularization; 3.1 Standard One-Step Linearization Methods; 3.2 Monotonicity-Based Regularization; 4 Numerical Results; 4.1 Experiment Setting; 4.2 Numerical Implementation; 4.3 Minimizing the Residuum; 5 Conclusions; References; An SVD in Spherical Surface Wave Tomography; 1 Introduction; 2 Fourier Analysis on S2 and SO(3); 2.1 Harmonic Analysis on the Sphere; 2.2 Rotational Harmonics; 2.3 Singular Value Decomposition; 3 Circle Arcs.
• Publisher Details: Cham, Switzerland : Birkhäuser
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 511/.8; Mathematics; Mathematical models -- Congresses; MATHEMATICS -- General; Mathematical models; Mathematics -- Functional Analysis; Mathematics -- Calculus; Mathematics -- Number Systems; Functional analysis & transforms; Calculus of variations; Numerical analysis; Differential equations, partial; Operator theory; Mathematical optimization; Numerical analysis; Mathematics -- Differential Equations; Differential calculus & equations; Electronic books; Conference papers and proceedings
• Languages: English
• ISBNs: 9783319708249; 3319708244
• Related ISBNs: 9783319708232; 3319708236
• Notes: Note: Online resource; title from PDF title page (SpringerLink, viewed February 19, 2018).
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