Download or read book Least Squares Methods for Linear Programming Problems written by Balaji Gopalakrishnan and published by LAP Lambert Academic Publishing. This book was released on 2011-06 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear programming has evolved over the years, due tosustained research and testing, as an excellent mathematical tool for solving manytheoretical and practical problems.Yet, escalating problem sizes in practical problemspose serious challenges for the verybest linear programming codes, running on the fastestcomputing hardware. New linearprogramming solution techniques have to developed tomeet these challenges. Theresearch performed in this book intends to addressthis issue through a comprehensivestudy of least-squares methods for solving linearprogramming problems.We have developed two new linear programmingalgorithms based on least-squarestheory. A Combined Objectives Least-Squares (COLS)algorithm uses a Non-NegativeLeast-Squares (NNLS) algorithm framework for solvingboth the Phase I and Phase IIlinear programming problems. A Least-SquaresPrimal-Dual (LSPD) algorithm usesNNLS solutions by solving small NNLS problems tosolve relatively larger linear programmingproblems. These algorithms are impervious todegeneracy. Computationalresults for the algorithms shows a superiorperformance over the simplex algorithmon a wide range of linear programming problems
Download or read book Least squares Methods for Solving Linear Programming Problems written by Balaji Gopalakrishnan and published by . This book was released on 2002 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 Optimal Solutions to Classes of Linear Programming Problems Using Modified Least Squares Techniques written by Richard Lee Rockett and published by . This book was released on 1974 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 302 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 Numerical Linear Algebra and Optimization written by Philip E. Gill and published by SIAM. This book was released on 2021-05-13 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic volume covers the fundamentals of two closely related topics: linear systems (linear equations and least-squares) and linear programming (optimizing a linear function subject to linear constraints). For each problem class, stable and efficient numerical algorithms intended for a finite-precision environment are derived and analyzed. While linear algebra and optimization have made huge advances since this book first appeared in 1991, the fundamental principles have not changed. These topics were rarely taught with a unified perspective, and, somewhat surprisingly, this remains true 30 years later. As a result, some of the material in this book can be difficult to find elsewhere—in particular, techniques for updating the LU factorization, descriptions of the simplex method applied to all-inequality form, and the analysis of what happens when using an approximate inverse to solve Ax=b. Numerical Linear Algebra and Optimization is primarily a reference for students who want to learn about numerical techniques for solving linear systems and/or linear programming using the simplex method; however, Chapters 6, 7, and 8 can be used as the text for an upper-division course on linear least squares and linear programming. Understanding is enhanced by numerous exercises.
Download or read book Linear Programming Algorithms Using Least squares Method written by Seunghyun Kong and published by . This book was released on 2007 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our computational results show that the least-squares primal-dual algorithm and the combined-objective least-squares algorithm perform better than the CPLEX Primal solver, but are slower than the CPLEX Dual solver. The least-squares network flow algorithm performs as fast as the CPLEX Network solver.
Download or read book Iterative Methods for Large Linear and Nonlinear Least Squares Problems written by John E. Dennis and published by . This book was released on 1986 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: Under a grant to 8 graduate students the most exciting research accomplishment is a new trust region approach to global convergence for nonlinear programming problems. Testing has also begun on a variable metric variant of the Kamarkar linear programming algorithm that could be of great practical significance if very preliminary tests are any indication. Other interesting work has been a unified convergence analysis for the many variants of the conjugate gradient method, a convergence analysis of the popular Nelder-Mead algorithm, a novel use of interactive computer graphics to obtain user preferences in multi-objective optimization, a convergence analysis of the EM algorithm for mixture density estimation, and a survey of all the work done by researchers in various fields on nonlinear programming problems in which some subset of the variables always appear linearly.
Download or read book Linear Least Squares Computations written by Farebrother and published by Routledge. This book was released on 2018-05-02 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting numerous algorithms in a simple algebraic form so that the reader can easilytranslate them into any computer language, this volume gives details of several methodsfor obtaining accurate least squares estimates. It explains how these estimates may beupdated as new information becomes available and how to test linear hypotheses.Linear Least Squares Computations features many structured exercises that guidethe reader through the available algorithms, plus a glossary of commonly used terms anda bibliography of supplementary reading ... collects "ancient" and modem results onlinear least squares computations in a convenient single source . . . develops the necessarymatrix algebra in the context of multivariate statistics . .. only makes peripheral use ofconcepts such as eigenvalues and partial differentiation .. . interprets canonical formsemployed in computation ... discusses many variants of the Gauss, Laplace-Schmidt,Givens, and Householder algorithms ... and uses an empirical approach for the appraisalof algorithms.Linear Least Squares Computations serves as an outstanding reference forindustrial and applied mathematicians, statisticians, and econometricians, as well as atext for advanced undergraduate and graduate statistics, mathematics, and econometricscourses in computer programming, linear regression analysis, and applied statistics.
Download or read book On the Nonnegative Least Squares written by Claudio Prata Santiago and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this document, we study the nonnegative least squares primal-dual method for solving linear programming problems. In particular, we investigate connections between this primal-dual method and the classical Hungarian method for the assignment problem. Firstly, we devise a fast procedure for computing the unrestricted least squares solution of a bipartite matching problem by exploiting the special structure of the incidence matrix of a bipartite graph. Moreover, we explain how to extract a solution for the cardinality matching problem from the nonnegative least squares solution. We also give an efficient procedure for solving the cardinality matching problem on general graphs using the nonnegative least squares approach. Next we look into some theoretical results concerning the minimization of p-norms, and separable differentiable convex functions, subject to linear constraints described by node-arc incidence matrices for graphs. Our main result is the reduction of the assignment problem to a single nonnegative least squares problem. This means that the primal-dual approach can be made to converge in one step for the assignment problem. This method does not reduce the primal-dual approach to one step for general linear programming problems, but it appears to give a good starting dual feasible point for the general problem.
Download or read book Least Squares written by Fouad Sabry and published by One Billion Knowledgeable. This book was released on 2024-05-11 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is Least Squares The method of least squares is a parameter estimation method in regression analysis based on minimizing the sum of the squares of the residuals made in the results of each individual equation. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Least squares Chapter 2: Gauss-Markov theorem Chapter 3: Regression analysis Chapter 4: Ridge regression Chapter 5: Total least squares Chapter 6: Ordinary least squares Chapter 7: Weighted least squares Chapter 8: Simple linear regression Chapter 9: Generalized least squares Chapter 10: Linear least squares (II) Answering the public top questions about least squares. (III) Real world examples for the usage of least squares in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Least Squares.
Download or read book Least Squares Finite Element Methods written by Pavel B. Bochev and published by Springer Science & Business Media. This book was released on 2009-04-28 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.
Download or read book Data Analysis Using the Method of Least Squares written by John Wolberg and published by Springer Science & Business Media. This book was released on 2006-02-08 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops the full power of the least-squares method Enables engineers and scientists to apply the method to their specific problem Deals with linear as well as with non-linear least-squares, parametric as well as non-parametric methods
Download or read book Numerical Linear Approximation in C written by Nabih Abdelmalek and published by CRC Press. This book was released on 2008-05-19 with total page 964 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illustrating the relevance of linear approximation in a variety of fields, Numerical Linear Approximation in C presents a unique collection of linear approximation algorithms that can be used to analyze, model, and compress discrete data. Developed by the lead author, the algorithms have been successfully applied to several engineering projects at the National Research Council of Canada. Basing most of the algorithms on linear programming techniques, the book begins with an introductory section that covers applications, the simplex method, and matrices. The next three parts focus on various L1, Chebyshev, and least squares approximations, including one-sided, bounded variables, and piecewise. The final section presents the solution of underdetermined systems of consistent linear equations that are subject to different constraints on the elements of the unknown solution vector. Except in the preliminary section, all chapters include the C functions of the algorithms, along with drivers that contain numerous test case examples and results. The accompanying CD-ROM also provides the algorithms written in C code as well as the test drivers. To use the software, it is not required to understand the theory behind each function.
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 Stable and Efficient Solution of Weighted Least squares Problems with Applications in Interior Point Methods written by Patricia D. Hough and published by . This book was released on 1996 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
