Download or read book Numerical Methods for Least Squares Problems Second Edition written by Åke Björck and published by SIAM. This book was released on 2024-07-05 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of least squares, discovered by Gauss in 1795, is a principal tool for reducing the influence of errors when fitting a mathematical model to given observations. Applications arise in many areas of science and engineering. The increased use of automatic data capturing frequently leads to large-scale least squares problems. Such problems can be solved by using recent developments in preconditioned iterative methods and in sparse QR factorization. The first edition of Numerical Methods for Least Squares Problems was the leading reference on the topic for many years. The updated second edition stands out compared to other books on this subject because it provides an in-depth and up-to-date treatment of direct and iterative methods for solving different types of least squares problems and for computing the singular value decomposition. It also is unique because it covers generalized, constrained, and nonlinear least squares problems as well as partial least squares and regularization methods for discrete ill-posed problems. The bibliography of over 1,100 historical and recent references provides a comprehensive survey of past and present research in the field. This book will be of interest to graduate students and researchers in applied mathematics and to researchers working with numerical linear algebra applications.

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 Nonlinear Equations and Optimisation written by L.T. Watson and published by Gulf Professional Publishing. This book was released on 2001-03-28 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: After a review of historical developments in convergence analysis for Newton's and Newton-like methods, 18 papers deal in depth with various classical, or neo-classical approaches, as well as newer ideas on optimization and solving linear equations. A sampling of topics: truncated Newton methods, sequential quadratic programming for large- scale nonlinear optimization, and automatic differentiation of algorithms. This monograph, one of seven volumes in the set, is also published as the Journal of Computational and Applied Mathematics; v.124 (2000). Indexed only by author. c. Book News Inc.

Download or read book Numerical Methods for Least Squares Problems written by Ake Bjorck and published by SIAM. This book was released on 1996-12-01 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of least squares: the principal tool for reducing the influence of errors when fitting models to given observations.

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1975 with total page 978 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1986 with total page 1036 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Optimization for Learning and Control written by Anders Hansson and published by John Wiley & Sons. This book was released on 2023-06-20 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization for Learning and Control Comprehensive resource providing a masters’ level introduction to optimization theory and algorithms for learning and control Optimization for Learning and Control describes how optimization is used in these domains, giving a thorough introduction to both unsupervised learning, supervised learning, and reinforcement learning, with an emphasis on optimization methods for large-scale learning and control problems. Several applications areas are also discussed, including signal processing, system identification, optimal control, and machine learning. Today, most of the material on the optimization aspects of deep learning that is accessible for students at a Masters’ level is focused on surface-level computer programming; deeper knowledge about the optimization methods and the trade-offs that are behind these methods is not provided. The objective of this book is to make this scattered knowledge, currently mainly available in publications in academic journals, accessible for Masters’ students in a coherent way. The focus is on basic algorithmic principles and trade-offs. Optimization for Learning and Control covers sample topics such as: Optimization theory and optimization methods, covering classes of optimization problems like least squares problems, quadratic problems, conic optimization problems and rank optimization. First-order methods, second-order methods, variable metric methods, and methods for nonlinear least squares problems. Stochastic optimization methods, augmented Lagrangian methods, interior-point methods, and conic optimization methods. Dynamic programming for solving optimal control problems and its generalization to reinforcement learning. How optimization theory is used to develop theory and tools of statistics and learning, e.g., the maximum likelihood method, expectation maximization, k-means clustering, and support vector machines. How calculus of variations is used in optimal control and for deriving the family of exponential distributions. Optimization for Learning and Control is an ideal resource on the subject for scientists and engineers learning about which optimization methods are useful for learning and control problems; the text will also appeal to industry professionals using machine learning for different practical applications.

Download or read book Convex Optimization written by Stephen P. Boyd and published by Cambridge University Press. This book was released on 2004-03-08 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

Download or read book Location Estimation from the Ground Up written by Sivan Toledo and published by SIAM. This book was released on 2020-09-17 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The location of an object can often be determined from indirect measurements using a process called estimation. This book explains the mathematical formulation of location-estimation problems and the statistical properties of these mathematical models. It also presents algorithms that are used to resolve these models to obtain location estimates, including the simplest linear models, nonlinear models (location estimation using satellite navigation systems and estimation of the signal arrival time from those satellites), dynamical systems (estimation of an entire path taken by a vehicle), and models with integer ambiguities (GPS location estimation that is centimeter-level accurate). Location Estimation from the Ground Up clearly presents analytic and algorithmic topics not covered in other books, including simple algorithms for Kalman filtering and smoothing, the solution of separable nonlinear optimization problems, estimation with integer ambiguities, and the implicit-function approach to estimating covariance matrices when the estimator is a minimizer or maximizer. It takes a unified approach to estimation while highlighting the differences between classes of estimation problems. The only book on estimation written for math and computer science students and graduates, it includes problems at the end of each chapter, many with solutions, to help readers deepen their understanding of the material and guide them through small programming projects that apply theory and algorithms to the solution of real-world location-estimation problems. The book’s core audience consists of engineers, including software engineers and algorithm developers, and graduate students who work on location-estimation projects and who need help translating the theory into algorithms, code, and deep understanding of the problem in front of them. Instructors in mathematics, computer science, and engineering may also find the book of interest as a primary or supplementary text for courses in location estimation and navigation.

Download or read book Compact Numerical Methods for Computers written by John C. Nash and published by CRC Press. This book was released on 1990-01-01 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition of Compact Numerical Methods for Computers presents reliable yet compact algorithms for computational problems. As in the previous edition, the author considers specific mathematical problems of wide applicability, develops approaches to a solution and the consequent algorithm, and provides the program steps. He emphasizes useful applicable methods from various scientific research fields, ranging from mathematical physics to commodity production modeling. While the ubiquitous personal computer is the particular focus, the methods have been implemented on computers as small as a programmable pocket calculator and as large as a highly parallel supercomputer. New to the Second Edition Presents program steps as Turbo Pascal code Includes more algorithmic examples Contains an extended bibliography The accompanying software (available by coupon at no charge) includes not only the algorithm source codes, but also driver programs, example data, and several utility codes to help in the software engineering of end-user programs. The codes are designed for rapid implementation and reliable use in a wide variety of computing environments. Scientists, statisticians, engineers, and economists who prepare/modify programs for use in their work will find this resource invaluable. Moreover, since little previous training in numerical analysis is required, the book can also be used as a supplementary text for courses on numerical methods and mathematical software.

Download or read book Least Squares Data Fitting with Applications written by Per Christian Hansen and published by JHU Press. This book was released on 2013-01-15 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: A lucid explanation of the intricacies of both simple and complex least squares methods. As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data predictively. The main concern of Least Squares Data Fitting with Applications is how to do this on a computer with efficient and robust computational methods for linear and nonlinear relationships. The presentation also establishes a link between the statistical setting and the computational issues. In a number of applications, the accuracy and efficiency of the least squares fit is central, and Per Christian Hansen, Víctor Pereyra, and Godela Scherer survey modern computational methods and illustrate them in fields ranging from engineering and environmental sciences to geophysics. Anyone working with problems of linear and nonlinear least squares fitting will find this book invaluable as a hands-on guide, with accessible text and carefully explained problems. Included are • an overview of computational methods together with their properties and advantages • topics from statistical regression analysis that help readers to understand and evaluate the computed solutions • many examples that illustrate the techniques and algorithms Least Squares Data Fitting with Applications can be used as a textbook for advanced undergraduate or graduate courses and professionals in the sciences and in engineering.

Download or read book Numerical Optimization written by Jorge Nocedal and published by Springer Science & Business Media. This book was released on 2006-12-11 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.

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 Nonlinear Parameter Optimization Using R Tools written by John C. Nash and published by John Wiley & Sons. This book was released on 2014-05-27 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Parameter Optimization Using R John C. Nash, Telfer School of Management, University of Ottawa, Canada A systematic and comprehensive treatment of optimization software using R In recent decades, optimization techniques have been streamlined by computational and artificial intelligence methods to analyze more variables, especially under non–linear, multivariable conditions, more quickly than ever before. Optimization is an important tool for decision science and for the analysis of physical systems used in engineering. Nonlinear Parameter Optimization with R explores the principal tools available in R for function minimization, optimization, and nonlinear parameter determination and features numerous examples throughout. Nonlinear Parameter Optimization with R: Provides a comprehensive treatment of optimization techniques Examines optimization problems that arise in statistics and how to solve them using R Enables researchers and practitioners to solve parameter determination problems Presents traditional methods as well as recent developments in R Is supported by an accompanying website featuring R code, examples and datasets Researchers and practitioners who have to solve parameter determination problems who are users of R but are novices in the field optimization or function minimization will benefit from this book. It will also be useful for scientists building and estimating nonlinear models in various fields such as hydrology, sports forecasting, ecology, chemical engineering, pharmaco-kinetics, agriculture, economics and statistics.

Download or read book Large Scale Nonlinear Optimization written by Gianni Pillo and published by Springer Science & Business Media. This book was released on 2006-06-03 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research. Individual chapters, contributed by eminent authorities, provide an up-to-date overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications.

Download or read book Computational Collective IntelligenceTechnologies and Applications written by Piotr Jedrzejowicz and published by Springer. This book was released on 2011-09-15 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNAI 6922 and LNAI 6923 constitutes the refereed proceedings of the Third International Conference on Computational Collective Intelligence, ICCCI 2011, held in Gdynia, Poland, in September 2011. The 112 papers in this two volume set presented together with 3 keynote speeches were carefully reviewed and selected from 300 submissions. The papers are organized in topical sections on knowledge management, machine learning and applications, autonomous and collective decision-making, collective computations and optimization, Web services and semantic Web, social networks and computational swarm intelligence and applications.

Download or read book High Performance Algorithms and Software for Nonlinear Optimization written by Gianni Pillo and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the edited texts of the lectures presented at the Workshop on High Performance Algorithms and Software for Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 30 - July 8, 2001. In the first year of the new century, the aim of the Workshop was to assess the past and to discuss the future of Nonlinear Optimization, and to highlight recent achieve ments and promising research trends in this field. An emphasis was requested on algorithmic and high performance software developments and on new computational experiences, as well as on theoretical advances. We believe that such goal was basically achieved. The Workshop was attended by 71 people from 22 countries. Although not all topics were covered, the presentations gave indeed a wide overview of the field, from different and complementary stand points. Besides the lectures, several formal and informal discussions took place. We wish to express our appreciation for the active contribution of all the participants in the meeting. The 18 papers included in this volume represent a significant selection of the most recent developments in nonlinear programming theory and practice. They show that there is plenty of exciting ideas, implementation issues and new applications which produce a very fast evolution in the field.