Iterative Methods for Optimization

Iterative Methods for Optimization

Author: C. T. Kelley

Publisher: SIAM

Published: 1999-01-01

Total Pages: 195

ISBN-13: 9781611970920

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This book presents a carefully selected group of methods for unconstrained and bound constrained optimization problems and analyzes them in depth both theoretically and algorithmically. It focuses on clarity in algorithmic description and analysis rather than generality, and while it provides pointers to the literature for the most general theoretical results and robust software, the author thinks it is more important that readers have a complete understanding of special cases that convey essential ideas. A companion to Kelley's book, Iterative Methods for Linear and Nonlinear Equations (SIAM, 1995), this book contains many exercises and examples and can be used as a text, a tutorial for self-study, or a reference. Iterative Methods for Optimization does more than cover traditional gradient-based optimization: it is the first book to treat sampling methods, including the Hooke-Jeeves, implicit filtering, MDS, and Nelder-Mead schemes in a unified way, and also the first book to make connections between sampling methods and the traditional gradient-methods. Each of the main algorithms in the text is described in pseudocode, and a collection of MATLAB codes is available. Thus, readers can experiment with the algorithms in an easy way as well as implement them in other languages.


Computational Methods for Inverse Problems

Computational Methods for Inverse Problems

Author: Curtis R. Vogel

Publisher: SIAM

Published: 2002-01-01

Total Pages: 195

ISBN-13: 0898717574

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Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.


Mathematical Modeling in Optical Science

Mathematical Modeling in Optical Science

Author: Gang Bao

Publisher: SIAM

Published: 2001-01-01

Total Pages: 349

ISBN-13: 9780898717594

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This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of mathematical models and the design and analysis of new computational approaches. The book contains cutting-edge discourses on emerging technology in optics that provides significant challenges and opportunities for applied mathematicians, researchers, and engineers.


Handbook for Matrix Computations

Handbook for Matrix Computations

Author: Thomas F. Coleman

Publisher: SIAM

Published: 1988-01-01

Total Pages: 271

ISBN-13: 9781611971040

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Provides the user with a step-by-step introduction to Fortran 77, BLAS, LINPACK, and MATLAB. It is a reference that spans several levels of practical matrix computations with a strong emphasis on examples and "hands on" experience.


The Mathematics of Reservoir Simulation

The Mathematics of Reservoir Simulation

Author: Richard E. Ewing

Publisher: SIAM

Published: 2014-12-01

Total Pages: 195

ISBN-13: 0898716624

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This book describes the state of the art of the mathematical theory and numerical analysis of imaging. Some of the applications covered in the book include computerized tomography, magnetic resonance imaging, emission tomography, electron microscopy, ultrasound transmission tomography, industrial tomography, seismic tomography, impedance tomography, and NIR imaging.


The Mathematics of Combustion

The Mathematics of Combustion

Author: John D. Buckmaster

Publisher: SIAM

Published: 1985-01-01

Total Pages: 266

ISBN-13: 9781611971064

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This book delves into the rapidly changing area of combustion, in which asymptotic methods and bifurcation theory have made a significant impact as have the constant-density, small-heat-release models and other important contributions.


Multigrid Methods

Multigrid Methods

Author: Stephen F. McCormick

Publisher: SIAM

Published: 1987-12-01

Total Pages: 292

ISBN-13: 1611971888

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A thoughtful consideration of the current level of development of multigrid methods, this volume is a carefully edited collection of papers that addresses its topic on several levels. The first three chapters orient the reader who is familiar with standard numerical techniques to multigrid methods, first by discussing multigrid in the context of standard techniques, second by detailing the mechanics of use of the method, and third by applying the basic method to some current problems in fluid dynamics. The fourth chapter provides a unified development, complete with theory, of algebraic multigrid (AMG), which is a linear equation solver based on multigrid principles. The last chapter is an ambitious development of a very general theory of multigrid methods for variationally posed problems. Included as an appendix is the latest edition of the Multigrid Bibliography, an attempted compilation of all existing research publications on multigrid.