| Description |
1 online resource (395 p.) |
| Contents |
Cover -- Title Page -- Copyright Page -- Dedication -- Preface -- Table of Contents -- Contributors -- 1. All-At-Once Formulation Meets the Bayesian Approach: A Study of Two Prototypical Linear Inverse Problems -- 1.1 Introduction -- 1.1.1 Examples -- 1.2 Function Space Setting and Computation of Adjoints -- 1.2.1 Inverse Source Problem -- 1.2.2 Backwards Heat Problem -- 1.3 Analysis of the Eigenvalues -- 1.3.1 Inverse Source Problem -- 1.3.1.1 Analytic Computation of the Eigenvalues -- 1.3.1.2 Numerical Computation of the Eigenvalues -- 1.3.2 Backwards Heat Equation |
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1.3.2.1 Analytic Computation of the Eigenvalues -- 1.3.2.2 Numerical Computation of the Eigenvalues -- 1.4 Convergence Analysis -- 1.4.1 Fulfillment of the Link Condition for the All-At-Once-Formulation -- 1.5 Choice of Joint Priors -- 1.5.1 Block Diagonal Priors Satisfying Unilateral Link Estimates -- 1.5.2 Heuristic Choice of C0 for the Backwards Heat Problem -- 1.5.3 Priors for the Inverse Source Problem -- 1.5.4 Prior for the State Variable of the Backwards Heat Problem -- 1.6 Numerical Experiments -- 1.6.1 Lagrangian Method for Computing the Adjoint Based Hessian and Gradient |
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1.6.1.1 Inverse Source Problem -- 1.6.1.2 Backwards Heat Problem -- 1.6.2 Implementation -- 1.6.2.1 Inverse Source Problem -- 1.6.2.2 Backwards Heat Equation, Sampled Initial Condition -- 1.6.2.3 Backwards Heat Equation, Chosen Initial Condition -- 1.6.2.4 Backwards Heat Equation, Chosen Initial Condition, Prior Motivated by the Link Condition -- 1.7 Conclusions and Remarks -- References -- 2. On Iterated Tikhonov Kaczmarz Type Methods for Solving Systems of Linear Ill-posed Operator Equations -- 2.1 Introduction -- 2.2 A Range-relaxed Iterated Tikhonov Kaczmarz Method -- 2.2.1 Main Assumptions |
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2.2.2 Description of the Method -- 2.2.3 Preliminary Results -- 2.3 A Convergence Result for Exact Data -- 2.4 Numerical Experiments -- 2.5 Conclusions -- References -- 3. On Numerical Approximation of Optimal Control for Stokes Hemivariational Inequalities -- 3.1 Introduction -- 3.2 Notation and Preliminaries -- 3.3 Stokes Hemivariational Inequality and Optimal Control -- 3.4 Numerical Approximation of the Optimal Control Problem -- References -- 4. Nonlinear Tikhonov Regularization in Hilbert Scales with Oversmoothing Penalty: Inspecting Balancing Principles -- 4.1 Introduction |
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4.1.1 Hilbert Scales with Respect to an Unbounded Operator -- 4.1.2 Tikhonov Regularization with Smoothness Promoting Penalty -- 4.1.3 State of the Art -- 4.1.4 Goal of the Present Study -- 4.2 General Error Estimate for Tikhonov Regularization in Hilbert Scales with Oversmoothing Penalty -- 4.2.1 Smoothness in Terms of Source Conditions -- 4.2.2 Error Decomposition -- 4.3 Balancing Principles -- 4.3.1 Quasi-optimality -- 4.3.2 The Balancing Principles: Setup and Formulation -- 4.3.3 Discussion -- 4.3.4 Specific Impact on Oversmoothing Penalties |
| Notes |
Description based upon print version of record |
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4.4 Exponential Growth Model: Properties and Numerical Case Study |
| Form |
Electronic book
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| Author |
Khan, Akhtar A
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Migórski, Stanisław
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Sama, Miguel
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| ISBN |
9781000511727 |
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1000511723 |
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