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Discrete inverse and state estimation problems : with geophysical fluid applications
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ISBN: 0521854245 9780521854245 9780511535949 9781107406063 9780511219276 051121927X 0511219954 9780511219955 0511220634 9780511220630 9780511221248 051122124X 1280480076 9781280480072 0511535945 051121927X 1107165776 9781107165779 1107406064 051131695X Year: 2006 Publisher: Cambridge : Cambridge University Press,

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Abstract

The problems of making inferences about the natural world from noisy observations and imperfect theories occur in almost all scientific disciplines. This 2006 book addresses these problems using examples taken from geophysical fluid dynamics. It focuses on discrete formulations, both static and time-varying, known variously as inverse, state estimation or data assimilation problems. Starting with fundamental algebraic and statistical ideas, the book guides the reader through a range of inference tools including the singular value decomposition, Gauss-Markov and minimum variance estimates, Kalman filters and related smoothers, and adjoint (Lagrange multiplier) methods. The final chapters discuss a variety of practical applications to geophysical flow problems. Discrete Inverse and State Estimation Problems is an ideal introduction to the topic for graduate students and researchers in oceanography, meteorology, climate dynamics, and geophysical fluid dynamics. It is also accessible to a wider scientific audience; the only prerequisite is an understanding of linear algebra.

Qualitative Methods in Inverse Scattering Theory : An Introduction
Authors: ---
ISBN: 9783540288442 3540288449 3540312307 Year: 2006 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,

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Inverse scattering theory has been a particularly active and successful field in applied mathematics and engineering for the past twenty years. The increasing demands of imaging and target identification require new powerful and flexible techniques besides the existing weak scattering approximation or nonlinear optimization methods. One class of such methods comes under the general description of qualitative methods in inverse scattering theory. This textbook is an easily-accessible "class-tested" introduction to the field. It is accessible also to readers who are not professional mathematicians, thus making these new mathematical ideas in inverse scattering theory available to the wider scientific and engineering community.

Keywords

Inverse problems (Differential equations) --- Scattering (Mathematics) --- Qualitative research. --- Problèmes inversés (Equations différentielles) --- Dispersion (Mathématiques) --- Recherche qualitative --- Engineering. --- Mathematics. --- Electrodynamics. --- Engineering mathematics. --- Materials. --- Appl.Mathematics/Computational Methods of Engineering. --- Applications of Mathematics. --- Continuum Mechanics and Mechanics of Materials. --- Classical Electrodynamics, Wave Phenomena. --- Electronic and Computer Engineering. --- Differential equations --- Calculus --- Applied Mathematics --- Civil Engineering --- Engineering & Applied Sciences --- Civil & Environmental Engineering --- Mathematics --- Physical Sciences & Mathematics --- Qualitative theory --- Qualitative theory. --- Scattering theory (Mathematics) --- 517.91 Differential equations --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Optics. --- Continuum mechanics. --- Electrical engineering. --- Analysis. --- Optics and Electrodynamics. --- Electrical Engineering. --- Electric engineering --- Engineering --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Dynamics --- Physics --- Light --- Engineering analysis --- Mathematical analysis --- 517.1 Mathematical analysis --- Math --- Science --- Boundary value problems --- Differential equations, Partial --- Scattering operator --- Global analysis (Mathematics). --- Mechanics. --- Mechanics, Applied. --- Computer engineering. --- Mathematical and Computational Engineering. --- Solid Mechanics. --- Classical Electrodynamics. --- Computers --- Classical mechanics --- Newtonian mechanics --- Quantum theory --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Design and construction

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