This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite and in infinite dimension. Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research.
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From the Back Cover
This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and partial differential equations). Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. The term 'affine invariance' means that the presented algorithms and their convergence analysis are invariant under one out of four subclasses of affine transformations of the problem to be solved. Compared to traditional textbooks, the distinguishing affine invariance approach leads to shorter theorems and proofs and permits the construction of fully adaptive algorithms. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research.
About the Author
Peter Deuflhard is founder and head of the internationally renowned Zuse Institute Berlin (ZIB) and full professor of Numerical Analysis and Scientific Computing at the Free University of Berlin. He is a regular invited speaker at international conferences and universities as well as industry places all over the world.
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Inside This Book
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First Sentence:
This chapter is an elementary introduction into the general theme of this book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
affine covariance, iterative refinement sweeps, tangent continuation method, natural monotonicity test, natural level function, accuracy matching strategy, affine contravariant, local convergence domain, inner iterative solver, classical continuation method, asymptotic mesh independence, optimal damping factors, cascadic multigrid methods, trust region strategy, separable nonlinear least squares problems, damping strategy, trust region strategies, convergence monitor, space shuttle problem, computational estimates, affine conjugacy, affine covariant, parameter dependent systems, error oriented, secant condition Key Phrases - Capitalized Phrases (CAPs): (learn more)
Exercises Exercise, Convex Functional Descent New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter is an elementary introduction into the general theme of this book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
affine covariance, iterative refinement sweeps, tangent continuation method, natural monotonicity test, natural level function, accuracy matching strategy, affine contravariant, local convergence domain, inner iterative solver, classical continuation method, asymptotic mesh independence, optimal damping factors, cascadic multigrid methods, trust region strategy, separable nonlinear least squares problems, damping strategy, trust region strategies, convergence monitor, space shuttle problem, computational estimates, affine conjugacy, affine covariant, parameter dependent systems, error oriented, secant condition Key Phrases - Capitalized Phrases (CAPs): (learn more)
Exercises Exercise, Convex Functional Descent New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 31
books:
See all 31 books this book cites
5
books
cite this book:
- Numerical Analysis 1999 (Chapman & Hall/CRC Research Notes in Mathematics Series) by G.A. Watson in Back Matter (1), and Back Matter (2)
- Animal Farm by George Orwell on page 138
- Computational Methods in Optimization: A Unified Approach (Mathematics in Science and Engineering Ser. : Vol 77) by Author Unknown in Back Matter
- Computational Techniques for Ordinary Differential Equations by I. Gladwell in Back Matter
- Theory and Numerics of Differential Equations by James F. Blowey in Back Matter
See all 31 books this book cites
- Numerische Mathematik I: 3., Uberarbeitete Auflage (German Edition) by Peter Deuflhard in Back Matter
- Advances in Robot Kinematics: Mechanisms and Motion by Jadran Lenarcic on page 472
- Optimale Steuerung partieller Differentialgleichungen by Fredi Tröltzsch in Back Matter
- Theoretical Numerical Analysis: A Functional Analysis Framework (Texts in Applied Mathematics) by Kendall Atkinson in Back Matter
- Numerische Mathematik: Eine projektorientierte Einführung für Ingenieure, Mathematiker und Naturwissenschaftler (vieweg studium; Grundkurs Mathematik) (German Edition) by Matthias Bollhöfer in Back Matter
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