Numerical Methods for Unconstrained Optimization and Nonlinear Equations

Author: J. E. Dennis, Jr.,Robert B. Schnabel
Publisher: SIAM
ISBN: 0898713641
Category: Mathematics
Page: 378
View: 2165
A complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations.

Mathematical Tools for Physicists

Author: Michael Grinfeld
Publisher: John Wiley & Sons
ISBN: 3527411887
Category: Science
Page: 632
View: 600
The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Numerical Analysis: Historical Developments in the 20th Century

Author: C. Brezinski,L. Wuytack
Publisher: Elsevier
ISBN: 0444598588
Category: Mathematics
Page: 512
View: 1170
Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.htmlNumerical Analysis 2000'. An introductory survey paper deals with the history of the first courses on numerical analysis in several countries and with the landmarks in the development of important algorithms and concepts in the field.

Iterative Solution of Nonlinear Equations in Several Variables

Author: J. M. Ortega,W. C. Rheinboldt
Publisher: SIAM
ISBN: 0898714613
Category: Mathematics
Page: 572
View: 2386
Surveys the theoretical results on systems of nonlinear equations in finite dimension and the major iterative methods for their computational solution. Offers a research-level presentation of the principal results known in 1970. The results and proof techniques introduced still represent a solid basis for this topic.

The Linear Complementarity Problem

Author: Richard W. Cottle,Jong-Shi Pang,Richard E. Stone
Publisher: SIAM
ISBN: 0898716861
Category: Mathematics
Page: 184
View: 7983
A revised edition of the standard reference on the linear complementarity problem.

Iterative Methods for Optimization

Author: C. T. Kelley
Publisher: SIAM
ISBN: 9781611970920
Category: Iterative methods (Mathematics)
Page: 180
View: 2152
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.

Newton Methods for Nonlinear Problems

Affine Invariance and Adaptive Algorithms
Author: Peter Deuflhard
Publisher: Springer Science & Business Media
ISBN: 3642238998
Category: Mathematics
Page: 424
View: 8416
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.

Finite Difference Methods for Ordinary and Partial Differential Equations

Steady-State and Time-Dependent Problems
Author: Randall J. LeVeque
Publisher: SIAM
ISBN: 9780898717839
Category: Differential equations
Page: 339
View: 5297
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

Numerical Methods and Optimization in Finance

Author: Manfred Gilli,Dietmar Maringer,Enrico Schumann
Publisher: Academic Press
ISBN: 0123756634
Category: Mathematics
Page: 600
View: 9666
This book describes computational finance tools. It covers fundamental numerical analysis and computational techniques, such as option pricing, and gives special attention to simulation and optimization. Many chapters are organized as case studies around portfolio insurance and risk estimation problems. In particular, several chapters explain optimization heuristics and how to use them for portfolio selection and in calibration of estimation and option pricing models. Such practical examples allow readers to learn the steps for solving specific problems and apply these steps to others. At the same time, the applications are relevant enough to make the book a useful reference. Matlab and R sample code is provided in the text and can be downloaded from the book's website. Shows ways to build and implement tools that help test ideas Focuses on the application of heuristics; standard methods receive limited attention Presents as separate chapters problems from portfolio optimization, estimation of econometric models, and calibration of option pricing models

Nonlinear Programming

Sequential Unconstrained Minimization Techniques
Author: Anthony V. Fiacco,Garth P. McCormick
Publisher: SIAM
ISBN: 0898712548
Category: Mathematics
Page: 210
View: 1673
Analyzes the 'central' or 'dual' trajectory used by modern path following and primal/dual methods for convex / general linear programming.

Methods for Solving Systems of Nonlinear Equations

Second Edition
Author: Werner C. Rheinboldt
Publisher: SIAM
ISBN: 9781611970012
Category: Equations, Simultaneous
Page: 148
View: 3110
This second edition provides much-needed updates to the original volume. Like the first edition, it emphasizes the ideas behind the algorithms as well as their theoretical foundations and properties, rather than focusing strictly on computational details; at the same time, this new version is now largely self-contained and includes essential proofs. Additions have been made to almost every chapter, including an introduction to the theory of inexact Newton methods, a basic theory of continuation methods in the setting of differentiable manifolds, and an expanded discussion of minimization methods. New information on parametrized equations and continuation incorporates research since the first edition.

The Bulletin of Mathematics Books

Author: N.A
Publisher: N.A
Category: Mathematics
Page: N.A
View: 9278

Second-order and Nonsmooth Training Methods for Fuzzy Neural Networks

Author: Christian Eitzinger
Publisher: N.A
ISBN: 9783854872665
Category: Fuzzy systems
Page: 143
View: 2935

Practical optimization

Author: Philip E. Gill,Walter Murray,Margaret H. Wright
Publisher: Academic Pr
Category: Mathematics
Page: 401
View: 8149
Mathematics of Computing -- Numerical Analysis.

Solving Nonlinear Equations with Newton's Method

Author: C. T. Kelley
Publisher: SIAM
ISBN: 9780898718898
Category: Iterative methods (Mathematics)
Page: 104
View: 9029
This book on Newton's method is a user-oriented guide to algorithms and implementation. In just over 100 pages, it shows, via algorithms in pseudocode, in MATLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem, diagnose problems, and write an efficient solver or apply one written by others. It contains trouble-shooting guides to the major algorithms, their most common failure modes, and the likely causes of failure. It also includes many worked-out examples (available on the SIAM website) in pseudocode and a collection of MATLAB codes, allowing readers to experiment with the algorithms easily and implement them in other languages.

Numerical Analysis and Scientific Computation

(International Edition) with Maple 10 VP
Author: Jeffrey Leader
Publisher: Addison-Wesley
ISBN: 9781405836098
Page: N.A
View: 8108

Elementary Numerical Analysis

An Algorithmic Approach
Author: S. D. Conte,Carl De Boor
Publisher: SIAM
ISBN: 1611975204
Category: Electronic books
Page: 456
View: 2373
This book provides a thorough and careful introduction to the theory and practice of scientific computing at an elementary, yet rigorous, level, from theory via examples and algorithms to computer programs. The original FORTRAN programs have been rewritten in MATLAB and now appear in a new appendix and online, offering a modernized version of this classic reference for basic numerical algorithms.

Large Scale Systems

Theory and Applications 1998 (LSS '98) : a Proceedings Volume from the 8th IFAC/IFORS/IMACS/IFIP Symposium, Rio Patras, Greece, 15-17 July 1998
Author: Nick Theodore Koussoulas,Peter P. Groumpos
Publisher: N.A
ISBN: 9780080430348
Category: Large scale systems
Page: 1173
View: 7000
As the 21st century nears, there is a need to seriously reconsider many aspects of modeling and controlling large, complex, man-made systems. Integration of technologies and functions requires deep interdisciplinary expertise and technical breadth for successful implementation. Large scale systems theory can play a central role in this effort and it is a strongly held belief that this approach will continue to be of major importance in the future.


Modélisation Mathématique Et Analyse Numérique : M2N.. Mathematical modelling and numerical analysis
Author: EDP Sciences
Publisher: N.A
Category: Numerical analysis
Page: N.A
View: 3013