Numerical Methods For Solving Inverse Problems Of Mathematical Physics
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Numerical Methods for Solving Inverse Problems of Mathematical Physics
Author | : Alexander A. Samarskii,Peter N. Vabishchevich |
Publsiher | : Unknown |
Total Pages | : 450 |
Release | : 2007-01 |
Genre | : Differential equations, Partial |
ISBN | : 9004155236 |
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This book treats some particular inverse problems for time-dependent and time-independent equations often encountered in mathematical physics.
Numerical Methods for Solving Inverse Problems of Mathematical Physics
Author | : A. A. Samarskii,Petr N. Vabishchevich |
Publsiher | : Walter de Gruyter |
Total Pages | : 453 |
Release | : 2008-08-27 |
Genre | : Mathematics |
ISBN | : 9783110205794 |
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The main classes of inverse problems for equations of mathematical physics and their numerical solution methods are considered in this book which is intended for graduate students and experts in applied mathematics, computational mathematics, and mathematical modelling.
Methods for Solving Inverse Problems in Mathematical Physics
Author | : Global Express Ltd. Co.,Aleksey I. Prilepko,Dmitry G. Orlovsky,Igor A. Vasin |
Publsiher | : CRC Press |
Total Pages | : 736 |
Release | : 2000-03-21 |
Genre | : Mathematics |
ISBN | : 0824719875 |
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Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, applications of functional analysis, and semigroup theory.
Inverse Problems of Mathematical Physics
Author | : Mikhail M. Lavrent'ev,Alexander V. Avdeev,Viatcheslav I. Priimenko |
Publsiher | : Walter de Gruyter |
Total Pages | : 288 |
Release | : 2012-05-07 |
Genre | : Mathematics |
ISBN | : 9783110915525 |
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This monograph deals with the theory of inverse problems of mathematical physics and applications of such problems. Besides it considers applications and numerical methods of solving the problems under study. Descriptions of particular numerical experiments are also included.
Inverse Problems
Author | : Mathias Richter |
Publsiher | : Springer Nature |
Total Pages | : 281 |
Release | : 2021-01-05 |
Genre | : Mathematics |
ISBN | : 9783030593179 |
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This textbook is an introduction to the subject of inverse problems with an emphasis on practical solution methods and applications from geophysics. The treatment is mathematically rigorous, relying on calculus and linear algebra only; familiarity with more advanced mathematical theories like functional analysis is not required. Containing up-to-date methods, this book will provide readers with the tools necessary to compute regularized solutions of inverse problems. A variety of practical examples from geophysics are used to motivate the presentation of abstract mathematical ideas, thus assuring an accessible approach. Beginning with four examples of inverse problems, the opening chapter establishes core concepts, such as formalizing these problems as equations in vector spaces and addressing the key issue of ill-posedness. Chapter Two then moves on to the discretization of inverse problems, which is a prerequisite for solving them on computers. Readers will be well-prepared for the final chapters that present regularized solutions of inverse problems in finite-dimensional spaces, with Chapter Three covering linear problems and Chapter Four studying nonlinear problems. Model problems reflecting scenarios of practical interest in the geosciences, such as inverse gravimetry and full waveform inversion, are fully worked out throughout the book. They are used as test cases to illustrate all single steps of solving inverse problems, up to numerical computations. Five appendices include the mathematical foundations needed to fully understand the material. This second edition expands upon the first, particularly regarding its up-to-date treatment of nonlinear problems. Following the author’s approach, readers will understand the relevant theory and methodology needed to pursue more complex applications. Inverse Problems is ideal for graduate students and researchers interested in geophysics and geosciences.
Mathematical and Numerical Approaches for Multi Wave Inverse Problems
Author | : Larisa Beilina,Maïtine Bergounioux,Michel Cristofol,Anabela Da Silva,Amelie Litman |
Publsiher | : Springer Nature |
Total Pages | : 147 |
Release | : 2020-06-30 |
Genre | : Mathematics |
ISBN | : 9783030486341 |
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This proceedings volume gathers peer-reviewed, selected papers presented at the “Mathematical and Numerical Approaches for Multi-Wave Inverse Problems” conference at the Centre Internacional de Rencontres Mathématiques (CIRM) in Marseille, France, in April 2019. It brings the latest research into new, reliable theoretical approaches and numerical techniques for solving nonlinear and inverse problems arising in multi-wave and hybrid systems. Multi-wave inverse problems have a wide range of applications in acoustics, electromagnetics, optics, medical imaging, and geophysics, to name but a few. In turn, it is well known that inverse problems are both nonlinear and ill-posed: two factors that pose major challenges for the development of new numerical methods for solving these problems, which are discussed in detail. These papers will be of interest to all researchers and graduate students working in the fields of nonlinear and inverse problems and its applications.
Inverse Problems of Mathematical Physics
Author | : V. G. Romanov |
Publsiher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 248 |
Release | : 2018-11-05 |
Genre | : Mathematics |
ISBN | : 9783110926019 |
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No detailed description available for "Inverse Problems of Mathematical Physics".
Ill posed Problems of Mathematical Physics and Analysis
Author | : Mikhail Mikha_lovich Lavrent_ev,Vladimir Gavrilovich Romanov,Serge_ Petrovich Shishatski_ |
Publsiher | : American Mathematical Soc. |
Total Pages | : 300 |
Release | : 1986-12-31 |
Genre | : Mathematics |
ISBN | : 0821898140 |
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Physical formulations leading to ill-posed problems Basic concepts of the theory of ill-posed problems Analytic continuation Boundary value problems for differential equations Volterra equations Integral geometry Multidimensional inverse problems for linear differential equations