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Author : A. A. Samarskii
Publisher : Walter de Gruyter
Page : 453 pages
File Size : 24,1 MB
Release : 2008-08-27
Category : Mathematics
ISBN : 3110205793
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.
Author : Alexander A. Samarskii
Publisher :
Page : 450 pages
File Size : 18,52 MB
Release : 2007-01
Category : Differential equations, Partial
ISBN : 9789004155237
This book treats some particular inverse problems for time-dependent and time-independent equations often encountered in mathematical physics.
Author : Mikhail M. Lavrent'ev
Publisher : Walter de Gruyter
Page : 288 pages
File Size : 34,67 MB
Release : 2012-05-07
Category : Mathematics
ISBN : 3110915529
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.
Author : Larisa Beilina
Publisher : Springer Nature
Page : 147 pages
File Size : 46,53 MB
Release : 2020-06-30
Category : Mathematics
ISBN : 3030486346
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.
Author : Mikhail Mikha_lovich Lavrent_ev
Publisher : American Mathematical Soc.
Page : 300 pages
File Size : 21,56 MB
Release : 1986-12-31
Category : Mathematics
ISBN : 9780821898147
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
Author : Yanfei Wang
Publisher : Walter de Gruyter
Page : 552 pages
File Size : 35,72 MB
Release : 2012-10-30
Category : Mathematics
ISBN : 3110259052
Nowadays inverse problems and applications in science and engineering represent an extremely active research field. The subjects are related to mathematics, physics, geophysics, geochemistry, oceanography, geography and remote sensing, astronomy, biomedicine, and other areas of applications. This monograph reports recent advances of inversion theory and recent developments with practical applications in frontiers of sciences, especially inverse design and novel computational methods for inverse problems. The practical applications include inverse scattering, chemistry, molecular spectra data processing, quantitative remote sensing inversion, seismic imaging, oceanography, and astronomical imaging. The book serves as a reference book and readers who do research in applied mathematics, engineering, geophysics, biomedicine, image processing, remote sensing, and environmental science will benefit from the contents since the book incorporates a background of using statistical and non-statistical methods, e.g., regularization and optimization techniques for solving practical inverse problems.
Author : Mathias Richter
Publisher : Springer Nature
Page : 281 pages
File Size : 45,87 MB
Release : 2021-01-05
Category : Mathematics
ISBN : 3030593177
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.
Author : Alexander G. Ramm
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 26,13 MB
Release : 2005-12-19
Category : Technology & Engineering
ISBN : 0387232184
Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.
Author : David L. Colton
Publisher : SIAM
Page : 234 pages
File Size : 19,68 MB
Release : 1990-01-01
Category : Mathematics
ISBN : 9780898712520
Author : Vitalii P. Tanana
Publisher : Walter de Gruyter GmbH & Co KG
Page : 138 pages
File Size : 10,80 MB
Release : 2018-03-19
Category : Mathematics
ISBN : 3110577216
The book covers fundamentals of the theory of optimal methods for solving ill-posed problems, as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods described in the current book are used to solve a number of inverse problems in mathematical physics. Contents Modulus of continuity of the inverse operator and methods for solving ill-posed problems Lavrent’ev methods for constructing approximate solutions of linear operator equations of the first kind Tikhonov regularization method Projection-regularization method Inverse heat exchange problems