This book focuses on Augmented Lagrangian techniques for solving practical constrained optimization problems. The authors rigorously delineate mathematical convergence theory based on sequential optimality conditions ...
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ISBN:
(数字)9781611973365
ISBN:
(纸本)9781611973358
This book focuses on Augmented Lagrangian techniques for solving practical constrained optimization problems. The authors rigorously delineate mathematical convergence theory based on sequential optimality conditions and novel constraint qualifications. They also orient the book to practitioners by giving priority to results that provide insight on the practical behavior of algorithms and by providing geometrical and algorithmic interpretations of every mathematical result, and they fully describe a freely available computational package for constrained optimization and illustrate its usefulness with applications. Audience: The book is aimed at engineers, physicists, chemists, and other practitioners interested in full access to comprehensive and well-documented software for large-scale optimization as well as up-to-date convergence theory and its practical consequences. It will also be of interest to graduate and advanced undergraduate students in mathematics, computer science, applied mathematics, optimization, and numerical analysis.
This concise and comprehensive treatment of the basic theory of algebraic Riccati equations describes the classical as well as the more advanced algorithms for their solution in a manner that is accessible to both pra...
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ISBN:
(数字)9781611972092
ISBN:
(纸本)9781611972085
This concise and comprehensive treatment of the basic theory of algebraic Riccati equations describes the classical as well as the more advanced algorithms for their solution in a manner that is accessible to both practitioners and scholars. It is the first book in which nonsymmetric algebraic Riccati equations are treated in a clear and systematic way. Some proofs of theoretical results have been simplified and a unified notation has been adopted.
Readers will find
• a unified discussion of doubling algorithms, which are effective in solving algebraic Riccati equations.
• a detailed description of all classical and advanced algorithms for solving algebraic Riccati equations and their MATLAB® codes. This will help the reader gain an understanding of the computational issues and provide ready-to-use implementation of the different solution techniques.
Several very powerful numerical linear algebra techniques are available for solving problems in data mining and pattern recognition. This application-oriented book describes how modern matrix methods can be used to so...
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ISBN:
(数字)9780898718867
ISBN:
(纸本)9780898716269
Several very powerful numerical linear algebra techniques are available for solving problems in data mining and pattern recognition. This application-oriented book describes how modern matrix methods can be used to solve these problems, gives an introduction to matrix theory and decompositions, and provides students with a set of tools that can be modified for a particular application. Part I gives a short introduction to a few application areas before presenting linear algebra concepts and matrix decompositions that students can use in problem-solving environments such as MATLAB. In Part II, linear algebra techniques are applied to data mining problems. Part III is a brief introduction to eigenvalue and singular value algorithms. The applications discussed include classification of handwritten digits, text mining, text summarization, pagerank computations related to the Google search engine, and face recognition. Exercises and computer assignments are available on a Web page that supplements the book.
Inverse problems arise when we reconstruct a sharper image from a blurred one or reconstruct the underground mass density from measurements of the gravity above the ground. When we solve an inverse problem, we compute...
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ISBN:
(数字)9780898718836
ISBN:
(纸本)9780898716962
Inverse problems arise when we reconstruct a sharper image from a blurred one or reconstruct the underground mass density from measurements of the gravity above the ground. When we solve an inverse problem, we compute the source that gives rise to some observed data using a mathematical model for the relation between the source and the data. This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms. Discrete Inverse Problems: Insight and algorithms includes a number of tutorial exercises that give the reader hands-on experience with the methods, difficulties, and challenges associated with the treatment of inverse problems. It also includes examples and figures that illustrate the theory and algorithms. Audience: This book is written for graduate students, researchers, and professionals in engineering and other areas that depend on solving inverse problems with noisy data. The aim is to provide readers with enough background that they can solve simple inverse problems and read more advanced literature on the subject. Contents: Preface; List of Symbols; Chapter 1: Introduction and Motivation; Chapter 2: Meet the Fredholm Integral Equation of the First Kind; Chapter 3: Getting to Business: Discretizations of Linear Inverse Problems; Chapter 4: Computational Aspects: Regularization Methods; Chapter 5: Getting Serious: Choosing the Regularization Parameter; Chapter 6: Toward Real-World Problems: Iterative Regularization; Chapter 7: Regularization Methods at Work: Solving Real Problems; Chapter 8: Beyond the 2-Norm: The Use of Discrete Smoothing Norms; Appendix A: Linear Algebra Stuff; Appendix B: Symmetric Toeplitz-Plus-Hankel Matrices and the DCT; Appendix C: Early Work on Tikhonov Regularization ; Bibliography; Index
When we use a camera, we want the recorded image to be a faithful representation of the scene that we see, but every image is more or less blurry. In image deblurring, the goal is to recover the original, sharp image ...
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ISBN:
(数字)9780898718874
ISBN:
(纸本)9780898716184
When we use a camera, we want the recorded image to be a faithful representation of the scene that we see, but every image is more or less blurry. In image deblurring, the goal is to recover the original, sharp image by using a mathematical model of the blurring process. The key issue is that some information on the lost details is indeed present in the blurred image, but this idden� information can be recovered only if we know the details of the blurring process. Deblurring Images: Matrices, Spectra, and Filtering describes the deblurring algorithms and techniques collectively known as spectral filtering methods, in which the singular value decompositionr a similar decomposition with spectral propertiess used to introduce the necessary regularization or filtering in the reconstructed image. The concise MATLAB� implementations described in the book provide a template of techniques that can be used to restore blurred images from many applications.
Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms,...
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ISBN:
(数字)9780898718881
ISBN:
(纸本)9780898716139
Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages.
With a strong emphasis on MATLAB® and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.
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