Algorithms for Finding Zeros and Extrema of Functions Without Calculating Derivatives PDF Download
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Author: Richard P. Brent Publisher: ISBN: Category : Algorithms Languages : en Pages : 656
Book Description
Theorems are given concerning the order (i.e., rate) of convergence of a successive interpolation process for finding simple zeros of a function or its derivatives, using only function evaluations. Special cases include the successive linear interpolation process for finding zeros, and a parabolic interpolation process for finding turning points. Results on interpolation and finite differences include weakening the hypotheses of a theorem of Ralston on the derivative of the error in Lagrangian interpolation. The theoretical results are applied to given algorithms for finding zeros or local minima of functions of one variable, in the presence of rounding errors. The algorithms are guaranteed to converge nearly as fast as would bisection or Fibonacci search, and in most practical cases convergence is superlinear, and much faster than for bisection or Fibonacci search. (Author).
Author: Richard P. Brent Publisher: ISBN: Category : Algorithms Languages : en Pages : 656
Book Description
Theorems are given concerning the order (i.e., rate) of convergence of a successive interpolation process for finding simple zeros of a function or its derivatives, using only function evaluations. Special cases include the successive linear interpolation process for finding zeros, and a parabolic interpolation process for finding turning points. Results on interpolation and finite differences include weakening the hypotheses of a theorem of Ralston on the derivative of the error in Lagrangian interpolation. The theoretical results are applied to given algorithms for finding zeros or local minima of functions of one variable, in the presence of rounding errors. The algorithms are guaranteed to converge nearly as fast as would bisection or Fibonacci search, and in most practical cases convergence is superlinear, and much faster than for bisection or Fibonacci search. (Author).
Author: Richard P. Brent Publisher: ISBN: Category : Algorithms Languages : en Pages : 662
Book Description
Theorems are given concerning the order (i.e., rate) of convergence of a successive interpolation process for finding simple zeros of a function or its derivatives, using only function evaluations. Special cases include the successive linear interpolation process for finding zeros, and a parabolic interpolation process for finding turning points. Results on interpolation and finite differences include weakening the hypotheses of a theorem of Ralston on the derivative of the error in Lagrangian interpolation. The theoretical results are applied to given algorithms for finding zeros or local minima of functions of one variable, in the presence of rounding errors. The algorithms are guaranteed to converge nearly as fast as would bisection or Fibonacci search, and in most practical cases convergence is superlinear, and much faster than for bisection or Fibonacci search. (Author).
Author: Richard P. Brent Publisher: Courier Corporation ISBN: 0486143686 Category : Mathematics Languages : en Pages : 210
Book Description
DIVOutstanding text for graduate students and research workers proposes improvements to existing algorithms, extends their related mathematical theories, and offers details on new algorithms for approximating local and global minima. /div
Author: J.M. McNamee Publisher: Elsevier Inc. Chapters ISBN: 0128076976 Category : Mathematics Languages : en Pages : 150
Book Description
We discuss the secant method:where are initial guesses. In the Regula Falsi variation we start with initial guesses and such that ; after an iteration similar to the above we replace either a or b by the new value depending on which of or has the same sign as . Often one of the points gets “stuck,” and several variants such as the Illinois or Pegasus methods and variations are used to “unstick” it. We discuss convergence and efficiency of most of the methods considered. We treat methods involving quadratic of higher order interpolation and rational approximation. We also discuss the bisection method where again and we set . We replace a or b by c according to the sign of as in the Regula Falsi method. Various generalizations are described, including some for complex roots. Finally we consider hybrid methods involving two or more of the previously described methods.
Author: George B. Dantzig Publisher: Springer Science & Business Media ISBN: 0387226338 Category : Business & Economics Languages : en Pages : 462
Book Description
Encompassing all the major topics students will encounter in courses on the subject, the authors teach both the underlying mathematical foundations and how these ideas are implemented in practice. They illustrate all the concepts with both worked examples and plenty of exercises, and, in addition, provide software so that students can try out numerical methods and so hone their skills in interpreting the results. As a result, this will make an ideal textbook for all those coming to the subject for the first time. Authors' note: A problem recently found with the software is due to a bug in Formula One, the third party commercial software package that was used for the development of the interface. It occurs when the date, currency, etc. format is set to a non-United States version. Please try setting your computer date/currency option to the United States option . The new version of Formula One, when ready, will be posted on WWW.
Author: Donald E. Brown Publisher: Springer Science & Business Media ISBN: 9400922035 Category : Business & Economics Languages : en Pages : 503
Book Description
The purpose of this book is to introduce and explain research at the boundary between two fields that view problem solving from different perspectives. Researchers in operations research and artificial intelligence have traditionally remained separate in their activities. Recently, there has been an explosion of work at the border of the two fields, as members of both communities seek to leverage their activities and resolve problems that remain intractable to pure operations research or artificial intelligence techniques. This book presents representative results from this current flurry of activity and provides insights into promising directions for continued exploration. This book should be of special interest to researchers in artificial intelligence and operations research because it exposes a number of applications and techniques, which have benefited from the integration of problem solving strategies. Even researchers working on different applications or with different techniques can benefit from the descriptions contained here, because they provide insight into effective methods for combining approaches from the two fields. Additionally, researchers in both communities will find a wealth of pointers to challenging new problems and potential opportunities that exist at the interface between operations research and artificial intelligence. In addition to the obvious interest the book should have for members of the operations research and artificial intelligence communities, the papers here are also relevant to members of other research communities and development activities that can benefit from improvements to fundamental problem solving approaches.
Author: George B. Dantzig Publisher: Springer Science & Business Media ISBN: 0387215697 Category : Mathematics Languages : en Pages : 461
Book Description
George Dantzig is widely regarded as the founder of this subject with his invention of the simplex algorithm in the 1940's. In this second volume, the theory of the items discussed in the first volume is expanded to include such additional advanced topics as variants of the simplex method; interior point methods, GUB, decomposition, integer programming, and game theory. Graduate students in the fields of operations research, industrial engineering and applied mathematics will thus find this volume of particular interest.
Author: Raymond Chan Publisher: OUP Oxford ISBN: 9780199206810 Category : Mathematics Languages : en Pages : 584
Book Description
The text presents and discusses some of the most influential papers in Matrix Computation authored by Gene H. Golub, one of the founding fathers of the field. The collection of 21 papers is divided into five main areas: iterative methods for linear systems, solution of least squares problems, matrix factorizations and applications, orthogonal polynomials and quadrature, and eigenvalue problems. Commentaries for each area are provided by leading experts: Anne Greenbaum, Ake Bjorck, Nicholas Higham, Walter Gautschi, and G. W. (Pete) Stewart. Comments on each paper are also included by the original authors, providing the reader with historical information on how the paper came to be written and under what circumstances the collaboration was undertaken. Including a brief biography and facsimiles of the original papers, this text will be of great interest to students and researchers in numerical analysis and scientific computation.
Author: Richard P. Brent
Author: Richard P. Brent
Author: Richard P. Brent
Author: Richard P. Brent
Author: J.M. McNamee
Author: University of Michigan Computing Center
Author: George B. Dantzig
Author: Donald E. Brown
Author: George B. Dantzig
Author: Raymond Chan
Author: Institute of Mathematics and Its Applications