{"product_id":"numerical-methods-for-inverse-problems-hardback-9781848218185","title":"Numerical Methods for Inverse Problems (Hardback) 9781848218185","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eNumerical Methods for Inverse Problems\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eMichel Kern (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781848218185, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 8 April 2016\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e240 pages\u003cbr\u003e24.1 x 16.3 x 1.8 cm, 0.499 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\"The book is very carefully written, in a reader-friendly style. It can be considered as an introductory textbook for the theory of ill-posed problems and their numerical solution.\" (\u003ci\u003eMathematical Reviews\/MathSciNet\u003c\/i\u003e 11\/05\/2017)\u003c\/p\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eThis book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the parameters of a physical system.\u003c\/p\u003e \u003cp\u003eThe author uses practical examples to illustrate inverse problems in physical sciences. He presents the techniques and specific methods chosen to solve inverse problems in a general domain of application, choosing to focus on a small number of methods that can be used in most applications.\u003c\/p\u003e \u003cp\u003eThis book is aimed at readers with a mathematical and scientific computing background. Despite this, it is a book with a practical perspective. The methods described are applicable, have been applied, and are often illustrated by numerical examples.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003ePreface ix\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 1 Introduction and Examples 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1 Overview of Inverse Problems 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1. Direct and inverse problems 3\u003c\/p\u003e \u003cp\u003e1.2. Well-posed and ill-posed problems 4\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2 Examples of Inverse Problems 9\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1. Inverse problems in heat transfer 10\u003c\/p\u003e \u003cp\u003e2.2. Inverse problems in hydrogeology 13\u003c\/p\u003e \u003cp\u003e2.3. Inverse problems in seismic exploration 16\u003c\/p\u003e \u003cp\u003e2.4. Medical imaging 21\u003c\/p\u003e \u003cp\u003e2.5. Other examples 25\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 2 Linear Inverse Problems 29\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3 Integral Operators and Integral Equations 31\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1. Definition and first properties 31\u003c\/p\u003e \u003cp\u003e3.2. Discretization of integral equations 36\u003c\/p\u003e \u003cp\u003e3.2.1. Discretization by quadrature–collocation 36\u003c\/p\u003e \u003cp\u003e3.2.2. Discretization by the Galerkin method 39\u003c\/p\u003e \u003cp\u003e3.3. Exercises 42\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4 Linear Least Squares Problems – Singular Value Decomposition 45\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1. Mathematical properties of least squares problems 45\u003c\/p\u003e \u003cp\u003e4.1.1. Finite dimensional case 50\u003c\/p\u003e \u003cp\u003e4.2. Singular value decomposition for matrices 52\u003c\/p\u003e \u003cp\u003e4.3. Singular value expansion for compact operators 57\u003c\/p\u003e \u003cp\u003e4.4. Applications of the SVD to least squares problems 60\u003c\/p\u003e \u003cp\u003e4.4.1. The matrix case 60\u003c\/p\u003e \u003cp\u003e4.4.2. The operator case 63\u003c\/p\u003e \u003cp\u003e4.5. Exercises 65\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5 Regularization of Linear Inverse Problems 71\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1. Tikhonov’s method 72\u003c\/p\u003e \u003cp\u003e5.1.1. Presentation 72\u003c\/p\u003e \u003cp\u003e5.1.2. Convergence 73\u003c\/p\u003e \u003cp\u003e5.1.3. The L-curve 81\u003c\/p\u003e \u003cp\u003e5.2. Applications of the SVE 83\u003c\/p\u003e \u003cp\u003e5.2.1. SVE and Tikhonov’s method 84\u003c\/p\u003e \u003cp\u003e5.2.2. Regularization by truncated SVE 85\u003c\/p\u003e \u003cp\u003e5.3. Choice of the regularization parameter 88\u003c\/p\u003e \u003cp\u003e5.3.1. Morozov’s discrepancy principle 88\u003c\/p\u003e \u003cp\u003e5.3.2. The L-curve 91\u003c\/p\u003e \u003cp\u003e5.3.3. Numerical methods 92\u003c\/p\u003e \u003cp\u003e5.4. Iterative methods 94\u003c\/p\u003e \u003cp\u003e5.5. Exercises 98\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart 3 Nonlinear Inverse Problems 103\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6 Nonlinear Inverse Problems – Generalities 105\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1. The three fundamental spaces 106\u003c\/p\u003e \u003cp\u003e6.2. Least squares formulation 111\u003c\/p\u003e \u003cp\u003e6.2.1. Difficulties of inverse problems 114\u003c\/p\u003e \u003cp\u003e6.2.2. Optimization, parametrization, discretization 114\u003c\/p\u003e \u003cp\u003e6.3. Methods for computing the gradient – the adjoint state method 116\u003c\/p\u003e \u003cp\u003e6.3.1. The finite difference method 116\u003c\/p\u003e \u003cp\u003e6.3.2. Sensitivity functions 118\u003c\/p\u003e \u003cp\u003e6.3.3. The adjoint state method 119\u003c\/p\u003e \u003cp\u003e6.3.4. Computation of the adjoint state by the Lagrangian 120\u003c\/p\u003e \u003cp\u003e6.3.5. The inner product test 123\u003c\/p\u003e \u003cp\u003e6.4. Parametrization and general organization 123\u003c\/p\u003e \u003cp\u003e6.5. Exercises 125\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7 Some Parameter Estimation Examples 127\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1. Elliptic equation in one dimension 127\u003c\/p\u003e \u003cp\u003e7.1.1. Computation of the gradient 128\u003c\/p\u003e \u003cp\u003e7.2. Stationary diffusion: elliptic equation in two dimensions 129\u003c\/p\u003e \u003cp\u003e7.2.1. Computation of the gradient: application of the general method 132\u003c\/p\u003e \u003cp\u003e7.2.2. Computation of the gradient by the Lagrangian 134\u003c\/p\u003e \u003cp\u003e7.2.3. The inner product test 135\u003c\/p\u003e \u003cp\u003e7.2.4. Multiscale parametrization 135\u003c\/p\u003e \u003cp\u003e7.2.5. Example 136\u003c\/p\u003e \u003cp\u003e7.3. Ordinary differential equations 137\u003c\/p\u003e \u003cp\u003e7.3.1. An application example 144\u003c\/p\u003e \u003cp\u003e7.4. Transient diffusion: heat equation 147\u003c\/p\u003e \u003cp\u003e7.5. Exercises 152\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8 Further Information 155\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1. Regularization in other norms 155\u003c\/p\u003e \u003cp\u003e8.1.1. Sobolev semi-norms 155\u003c\/p\u003e \u003cp\u003e8.1.2. Bounded variation regularization norm 157\u003c\/p\u003e \u003cp\u003e8.2. Statistical approach: Bayesian inversion 157\u003c\/p\u003e \u003cp\u003e8.2.1. Least squares and statistics 158\u003c\/p\u003e \u003cp\u003e8.2.2. Bayesian inversion 160\u003c\/p\u003e \u003cp\u003e8.3. Other topics 163\u003c\/p\u003e \u003cp\u003e8.3.1. Theoretical aspects: identifiability 163\u003c\/p\u003e \u003cp\u003e8.3.2. Algorithmic differentiation 163\u003c\/p\u003e \u003cp\u003e8.3.3. Iterative methods and large-scale problems 164\u003c\/p\u003e \u003cp\u003e8.3.4. Software 164\u003c\/p\u003e \u003cp\u003eAppendices 167\u003c\/p\u003e \u003cp\u003eAppendix 1 169\u003c\/p\u003e \u003cp\u003eAppendix 2 183\u003c\/p\u003e \u003cp\u003eAppendix 3 193\u003c\/p\u003e \u003cp\u003eBibliography 205\u003c\/p\u003e \u003cp\u003eIndex 213\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley-ISTE","offers":[{"title":"Brand New","offer_id":52449392853272,"sku":"9781848218185","price":100.57,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781848218185.jpg?v=1785197891","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/numerical-methods-for-inverse-problems-hardback-9781848218185","provider":"Freshly Printed Books","version":"1.0","type":"link"}