Download or read book Solving Linear Least Squares with Broyden s Method written by Richard Rand Gerber and published by . This book was released on 1981 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Iterative Methods for Linear and Nonlinear Equations written by C. T. Kelley and published by SIAM. This book was released on 1995-01-01 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.

Download or read book A Mathematical Introduction to Electronic Structure Theory written by Lin Lin and published by SIAM. This book was released on 2019-06-05 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on first principle quantum mechanics, electronic structure theory is widely used in physics, chemistry, materials science, and related fields and has recently received increasing research attention in applied and computational mathematics. This book provides a self-contained, mathematically oriented introduction to the subject and its associated algorithms and analysis. It will help applied mathematics students and researchers with minimal background in physics understand the basics of electronic structure theory and prepare them to conduct research in this area. The book begins with an elementary introduction of quantum mechanics, including the uncertainty principle and the Hartree?Fock theory, which is considered the starting point of modern electronic structure theory. The authors then provide an in-depth discussion of two carefully selected topics that are directly related to several aspects of modern electronic structure calculations: density matrix based algorithms and linear response theory. Chapter 2 introduces the Kohn?Sham density functional theory with a focus on the density matrix based numerical algorithms, and Chapter 3 introduces linear response theory, which provides a unified viewpoint of several important phenomena in physics and numerics. An understanding of these topics will prepare readers for more advanced topics in this field. The book concludes with the random phase approximation to the correlation energy. The book is written for advanced undergraduate and beginning graduate students, specifically those with mathematical backgrounds but without a priori knowledge of quantum mechanics, and can be used for self-study by researchers, instructors, and other scientists. The book can also serve as a starting point to learn about many-body perturbation theory, a topic at the frontier of the study of interacting electrons.

Download or read book Numerical methods for scientists and engineers written by H. M. Antia and published by Springer. This book was released on 2012-11-15 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an exhaustive and in-depth exposition of the various numerical methods used in scientific and engineering computations. It emphasises the practical aspects of numerical computation and discusses various techniques in sufficient detail to enable their implementation in solving a wide range of problems. The main addition in the third edition is a new Chapter on Statistical Inferences. There is also some addition and editing in the next chapter on Approximations. With this addition 12 new programs have also been added.

Download or read book Numerical Methods for Unconstrained Optimization and Nonlinear Equations written by J. E. Dennis, Jr. and published by SIAM. This book was released on 1996-12-01 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.

Download or read book Encyclopedia of Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2008-09-04 with total page 4646 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Download or read book Mathematics for Large Scale Computing written by Julio Diaz and published by CRC Press. This book was released on 2020-06-29 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: During recent years a great deal of interest has been devoted to large scale computing applications. This has occurred in great part because of the introduction of advanced high performance computer architectures. The book contains survey articles as well as chapters on specific research applications, development and analysis of numerical algorithms, and performance evaluation of algorithms on advanced architectures. The effect of specialized architectural features on the performance of large scale computation is also considered by several authors. Several areas of applications are represented, including the numerical solution of partial differential equations, iterative techniques for large structured problems, the numerical solution of boundary value problems for ordinary differential equations, numerical optimization, and numerical quadrature. Mathematical issues in computer architecture are also presented, including the description of grey codes for generalized hypercubes. The results presented in this volume give, in our opinion, a representative picture of today’s state of the art in several aspects of large scale computing.

Download or read book Iterative Methods for Optimization written by C. T. Kelley and published by SIAM. This book was released on 1999-01-01 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book System Modeling and Optimization written by Lorena Bociu and published by Springer. This book was released on 2017-04-10 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of thoroughly refereed papers presented at the 27th IFIP TC 7 Conference on System Modeling and Optimization, held in Sophia Antipolis, France, in June/July 2015. The 48 revised papers were carefully reviewed and selected from numerous submissions. They cover the latest progress in their respective areas and encompass broad aspects of system modeling and optimiza-tion, such as modeling and analysis of systems governed by Partial Differential Equations (PDEs) or Ordinary Differential Equations (ODEs), control of PDEs/ODEs, nonlinear optimization, stochastic optimization, multi-objective optimization, combinatorial optimization, industrial applications, and numericsof PDEs.

Download or read book Nonlinear Equations and Optimisation written by L.T. Watson and published by Elsevier. This book was released on 2001-03-14 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: /homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! In one of the papers in this collection, the remark that "nothing at all takes place in the universe in which some rule of maximum of minimum does not appear" is attributed to no less an authority than Euler. Simplifying the syntax a little, we might paraphrase this as Everything is an optimization problem. While this might be something of an overstatement, the element of exaggeration is certainly reduced if we consider the extended form: Everything is an optimization problem or a system of equations. This observation, even if only partly true, stands as a fitting testimonial to the importance of the work covered by this volume. Since the 1960s, much effort has gone into the development and application of numerical algorithms for solving problems in the two areas of optimization and systems of equations. As a result, many different ideas have been proposed for dealing efficiently with (for example) severe nonlinearities and/or very large numbers of variables. Libraries of powerful software now embody the most successful of these ideas, and one objective of this volume is to assist potential users in choosing appropriate software for the problems they need to solve. More generally, however, these collected review articles are intended to provide both researchers and practitioners with snapshots of the 'state-of-the-art' with regard to algorithms for particular classes of problem. These snapshots are meant to have the virtues of immediacy through the inclusion of very recent ideas, but they also have sufficient depth of field to show how ideas have developed and how today's research questions have grown out of previous solution attempts. The most efficient methods for local optimization, both unconstrained and constrained, are still derived from the classical Newton approach. As well as dealing in depth with the various classical, or neo-classical, approaches, the selection of papers on optimization in this volume ensures that newer ideas are also well represented. Solving nonlinear algebraic systems of equations is closely related to optimization. The two are not completely equivalent, however, and usually something is lost in the translation. Algorithms for nonlinear equations can be roughly classified as locally convergent or globally convergent. The characterization is not perfect. Locally convergent algorithms include Newton's method, modern quasi-Newton variants of Newton's method, and trust region methods. All of these approaches are well represented in this volume.

Download or read book Transactions on Engineering Technologies written by Sio-Iong Ao and published by Springer. This book was released on 2018-02-09 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of revised and extended research articles written by prominent researchers participating in the 25th International MultiConference of Engineers and Computer Scientists (IMECS 2017) which was held in Hong Kong, 15-17 March, 2017. Topics covered include electrical engineering, communications systems, engineering mathematics, engineering physics, and industrial applications. With contributions carefully chosen to represent the most cutting-edge research presented during the conference, the book offers the state of art in engineering technologies and physical science and applications, and also serves as an excellent reference work for researchers and graduate students working with/on engineering technologies and physical science and applications.

Download or read book Soft Computing in Industrial Applications written by Yukinori Suzuki and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains recent theoretical innovations and a comprehensive collection of industrial applications in the emerging field of Soft Computing. Soft computing is a new form of artificial intelligence and it consists of four core methodologies: Fuzzy Computing, Neuro Computing, Evolutionary Computation, and Probabilistic Computing. These individual techniques are clearly complementary or synergistic rather than competitive. Therefore, it is a common practice to combine two or three methodologies when solving complex problems. Also the systematic fusion of soft computing and hard computing is a highly potential alternative to be considered. Soft computing methodologies are suitable for various real-world applications, because the available information and system knowledge are often imprecise, un certain, or partially even incorrect. To handle such demanding conditions and obtain the required robustness with pure hard computing would typically be either very difficult or expensive. This book is a unique collection of technical articles providing a thorough overview of the state-of-the-art theory and industrial applications. The core articles on evolutionary computation, fuzzy computing, and neuro computing are of particular interest to researchers and practicing engineers.

Download or read book Computer Algorithms for Solving Linear Algebraic Equations written by Emilio Spedicato and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The NATO Advanced Study Institute on "Computer algorithms for solving linear algebraic equations: the state of the art" was held September 9-21, 1990, at II Ciocco, Barga, Italy. It was attended by 68 students (among them many well known specialists in related fields!) from the following countries: Belgium, Brazil, Canada, Czechoslovakia, Denmark, France, Germany, Greece, Holland, Hungary, Italy, Portugal, Spain, Turkey, UK, USA, USSR, Yugoslavia. Solving linear equations is a fundamental task in most of computational mathematics. Linear systems which are now encountered in practice may be of very large dimension and their solution can still be a challenge in terms of the requirements of accuracy or reasonable computational time. With the advent of supercomputers with vector and parallel features, algorithms which were previously formulated in a framework of sequential operations often need a completely new formulation, and algorithms that were not recommended in a sequential framework may become the best choice. The aim of the ASI was to present the state of the art in this field. While not all important aspects could be covered (for instance there is no presentation of methods using interval arithmetic or symbolic computation), we believe that most important topics were considered, many of them by leading specialists who have contributed substantially to the developments in these fields.

Download or read book Rock Joints written by Nick Barton and published by CRC Press. This book was released on 1990-01-01 with total page 844 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the International Symposium on Rock Joints held at Loen, Norway, June 1990. Subjects include geological aspects of joint origin and morphology, mechanical behaviour such as shear strength, hydraulic behaviour, and dynamic behaviour.

Download or read book Trust Region Methods written by A. R. Conn and published by SIAM. This book was released on 2000-01-01 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.

Download or read book Computational Solution of Nonlinear Systems of Equations written by Eugene L. Allgower and published by American Mathematical Soc.. This book was released on 1990-04-03 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear equations arise in essentially every branch of modern science, engineering, and mathematics. However, in only a very few special cases is it possible to obtain useful solutions to nonlinear equations via analytical calculations. As a result, many scientists resort to computational methods. This book contains the proceedings of the Joint AMS-SIAM Summer Seminar, ``Computational Solution of Nonlinear Systems of Equations,'' held in July 1988 at Colorado State University. The aim of the book is to give a wide-ranging survey of essentially all of the methods which comprise currently active areas of research in the computational solution of systems of nonlinear equations. A number of ``entry-level'' survey papers were solicited, and a series of test problems has been collected in an appendix. Most of the articles are accessible to students who have had a course in numerical analysis.

Download or read book Topics in Applied Multivariate Analysis written by D. M. Hawkins and published by Cambridge University Press. This book was released on 1982-04-22 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multivariate methods are employed widely in the analysis of experimental data but are poorly understood by those users who are not statisticians. This is because of the wide divergence between the theory and practice of multivariate methods. This book provides concise yet thorough surveys of developments in multivariate statistical analysis and gives statistically sound coverage of the subject. The contributors are all experienced in the theory and practice of multivariate methods and their aim has been to emphasize the major features from the point of view of applicability and to indicate the limitations and conditions of the techniques. Professional statisticians wanting to improve their background in applicable methods, users of high-level statistical methods wanting to improve their background in fundamentals, and graduate students of statistics will all find this volume of value and use.