Download or read book On the Successive Projections Approach to Least Squares Problems written by and published by . This book was released on 1985 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper suggests a generalized Gauss-Seidel approach to sparse linear and nonlinear least squares problems. The algorithm, closely related to one given by Elfving, uses the work of Curtis, Powell, and Reid as extended by Coleman and More) to divide the variables into nondisjoint groups of structurally orthogonal columns and then projects the updated residual into each column subspace of the Jacobian in turn. In the linear case, this procedure can be viewed as an alternate ordering of the variables in the Gauss-Seidel method. Preliminary tests indicate that this leads quickly to cheap solutions of limited accuracy for linear problems, and that this approach is promising for an inexact Gauss Newton analog of the inexact Newton approach of Dembo, Eisenstat, and Steihaug.
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 Research in Progress written by and published by . This book was released on 1984 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Lp Norm Estimation written by Rene Gonin and published by Routledge. This book was released on 2017-10-02 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complete with valuable FORTRAN programs that help solve nondifferentiable nonlinear LtandLo.-norm estimation problems, this important reference/text extensively delineates ahistory of Lp-norm estimation. It examines the nonlinear Lp-norm estimation problem that isa viable alternative to least squares estimation problems where the underlying errordistribution is nonnormal, i.e., non-Gaussian.Nonlinear LrNorm Estimation addresses both computational and statistical aspects ofLp-norm estimation problems to bridge the gap between these two fields . . . contains 70useful illustrations ... discusses linear Lp-norm as well as nonlinear Lt, Lo., and Lp-normestimation problems . . . provides all appropriate computational algorithms and FORTRANlistings for nonlinear Lt- and Lo.-norm estimation problems . . . guides readers with clear endof-chapter notes on related topics and outstanding research publications . . . contains numericalexamples plus several practical problems .. . and shows how the data can prescribe variousapplications of Lp-norm alternatives.Nonlinear Lp-Norm Estimation is an indispensable reference for statisticians,operations researchers, numerical analysts, applied mathematicians, biometricians, andcomputer scientists, as well as a text for graduate students in statistics or computer science.
Download or read book Solving Least Squares Problems written by Charles L. Lawson and published by SIAM. This book was released on 1995-12-01 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Classic edition includes a new appendix which summarizes the major developments since the book was originally published in 1974. The additions are organized in short sections associated with each chapter. An additional 230 references have been added, bringing the bibliography to over 400 entries. Appendix C has been edited to reflect changes in the associated software package and software distribution method.
Download or read book Euro Par 2004 Parallel Processing written by Marco Danelutto and published by Springer Science & Business Media. This book was released on 2004-08-19 with total page 1114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 10th International Conference on Parallel Computing, Euro-Par 2004, held in Pisa, Italy in August/September 2004. The 122 revised papers presented together with 3 invited papers were carefully reviewed and selected from 352 submissions. The papers are organized in topical sections on support tools and environments, performance evaluation, scheduling and load balancing, compilers and high performance, parallel and distributed databases, grid and cluster computing, applications on high performance clusters, parallel computer architecture and ILP, distributed systems and algorithms, parallel programming, numerical algorithms, high performance multimedia, theory and algorithms for parallel computing, routing and communication in interconnection networks, mobile computing, integrated problem solving environments, high performance bioinformatics, and peer-to-peer and Web computing.
Download or read book Successive Orthogonal Projections for Exact Computation of Minimal Norm Solution of Inconsistent and Rank defficient Least squares Problems written by Mekhon Ṿaitsman le-madaʻ. Dept. of Applied Mathematics and Computer Science and published by . This book was released on 1996 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "In the present paper we present a direct method for computation of the minimal norm solution of generally (inconsistent and rank-defficient) least-squares problems. The method is based on the classical Kaczmarz's iterative algorithm to which we attach a set of new directions for projection. The practical construction of these new directions together with comments concerning computational aspects are also presented, in the last section of the paper."
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 Scientific Computing written by John A. Trangenstein and published by Springer. This book was released on 2018-05-14 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses basic principles of computation, and fundamental numerical algorithms that will serve as basic tools for the subsequent two volumes. This book and its companions show how to determine the quality of computational results, and how to measure the relative efficiency of competing methods. Readers learn how to determine the maximum attainable accuracy of algorithms, and how to select the best method for computing problems. This book also discusses programming in several languages, including C++, Fortran and MATLAB. There are 80 examples, 324 exercises, 77 algorithms, 35 interactive JavaScript programs, 391 references to software programs and 4 case studies. Topics are introduced with goals, literature references and links to public software. There are descriptions of the current algorithms in LAPACK, GSLIB and MATLAB. This book could be used for an introductory course in numerical methods, for either upper level undergraduates or first year graduate students. Parts of the text could be used for specialized courses, such as principles of computer languages or numerical linear algebra.
Download or read book Euro Par 97 Parallel Processing written by Christian Lengauer and published by Springer. This book was released on 2005-11-23 with total page 1382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Euro-Par Conference, held in Passau, Germany, in August 1997. The 178 revised papers presented were selected from more than 300 submissions on the basis of 1101 reviews. The papers are organized in accordance with the conference workshop structure in tracks on support tools and environments, routing and communication, automatic parallelization, parallel and distributed algorithms, programming languages, programming models and methods, numerical algorithms, parallel architectures, HPC applications, scheduling and load balancing, performance evaluation, instruction-level parallelism, database systems, symbolic computation, real-time systems, and an ESPRIT workshop.
Download or read book Recursive Least Squares Algorithm for Linear Prediction Problems written by Sanzheng Qiao and published by . This book was released on 1986 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Alternating Projection Methods written by Ren Escalante and published by SIAM. This book was released on 2011-10-06 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive textbook for advanced undergraduate or graduate students.
Download or read book The Total Least Squares Problem written by Sabine Van Huffel and published by SIAM. This book was released on 1991-01-01 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book devoted entirely to total least squares. The authors give a unified presentation of the TLS problem. A description of its basic principles are given, the various algebraic, statistical and sensitivity properties of the problem are discussed, and generalizations are presented. Applications are surveyed to facilitate uses in an even wider range of applications. Whenever possible, comparison is made with the well-known least squares methods. A basic knowledge of numerical linear algebra, matrix computations, and some notion of elementary statistics is required of the reader; however, some background material is included to make the book reasonably self-contained.
Download or read book A Variable Projection Method for Solving Seperable Nonlinear Least Squares Problems written by L. Kaufman and published by . This book was released on 1974 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Numerical Analysis written by Philippe G. Ciarlet and published by North-Holland is. This book was released on 1990 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
