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Prompted by recent developments in inverse theory, this book is a completely rewritten version of a 1987 book by the same author. In this version there are many algorithmic details for Monte Carlo methods, least-squares discrete problems, and least-squares problems involving functions.
Reviews and extends the theory of Lie groups, develops differential geometry, proposing compact definitions of torsion and of curvature, and adapts the usual notion of linear tangent application to the intrinsic point of view proposed for physics.
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