Alternating Projection Methods
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Alternating Projection Methods
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Author : Ren Escalante
language : en
Publisher: SIAM
Release Date : 2011-10-06
Alternating Projection Methods written by Ren Escalante and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-06 with Mathematics categories.
A comprehensive textbook for advanced undergraduate or graduate students.
Alternating Projections Cat 0 Spaces
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Author : Miroslav Bačák
language : en
Publisher:
Release Date : 2011
Alternating Projections Cat 0 Spaces written by Miroslav Bačák and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
By using recently developed theory which extends the idea of weak convergence into CAT(0) space we prove the convergence of the alternating projection method for convex closed subsets of a CAT(0) space. Given the right notion of weak convergence it turns out that the generalization of the well-known results in Hilbert spaces is straightforward and allows the use of the method in a nonlinear setting. As an application, we use the alternating projection method to minimize convex functionals on a CAT(0) space.
Alternating Projection Methods For Calculating The Nearest Structured Matrix
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Author : 黃偉誠
language : en
Publisher:
Release Date : 2020
Alternating Projection Methods For Calculating The Nearest Structured Matrix written by 黃偉誠 and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
Projectors And Projection Methods
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Author : Aurél Galántai
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Projectors And Projection Methods written by Aurél Galántai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
The projectors are considered as simple but important type of matrices and operators. Their basic theory can be found in many books, among which Hal mas [177], [178] are of particular significance. The projectors or projections became an active research area in the last two decades due to ideas generated from linear algebra, statistics and various areas of algorithmic mathematics. There has also grown up a great and increasing number of projection meth ods for different purposes. The aim of this book is to give a unified survey on projectors and projection methods including the most recent results. The words projector, projection and idempotent are used as synonyms, although the word projection is more common. We assume that the reader is familiar with linear algebra and mathemati cal analysis at a bachelor level. The first chapter includes supplements from linear algebra and matrix analysis that are not incorporated in the standard courses. The second and the last chapter include the theory of projectors. Four chapters are devoted to projection methods for solving linear and non linear systems of algebraic equations and convex optimization problems.
Distributed Optimization And Statistical Learning Via The Alternating Direction Method Of Multipliers
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Author : Stephen Boyd
language : en
Publisher: Now Publishers Inc
Release Date : 2011
Distributed Optimization And Statistical Learning Via The Alternating Direction Method Of Multipliers written by Stephen Boyd and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Computers categories.
Surveys the theory and history of the alternating direction method of multipliers, and discusses its applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others.
Greedy Approximation
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Author : Vladimir Temlyakov
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-08
Greedy Approximation written by Vladimir Temlyakov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-08 with Computers categories.
This first book on greedy approximation gives a systematic presentation of the fundamental results. It also contains an introduction to two hot topics in numerical mathematics: learning theory and compressed sensing. Nonlinear approximation is becoming increasingly important, especially since two types are frequently employed in applications: adaptive methods are used in PDE solvers, while m-term approximation is used in image/signal/data processing, as well as in the design of neural networks. The fundamental question of nonlinear approximation is how to devise good constructive methods (algorithms) and recent results have established that greedy type algorithms may be the solution. The author has drawn on his own teaching experience to write a book ideally suited to graduate courses. The reader does not require a broad background to understand the material. Important open problems are included to give students and professionals alike ideas for further research.
Inverse Eigenvalue Problems
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Author : Moody Chu
language : en
Publisher: OUP Oxford
Release Date : 2005-06-16
Inverse Eigenvalue Problems written by Moody Chu and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-16 with Mathematics categories.
Inverse eigenvalue problems arise in a remarkable variety of applications and associated with any inverse eigenvalue problem are two fundamental questions—the theoretical issue of solvability and the practical issue of computability. Both questions are difficult and challenging. In this text, the authors discuss the fundamental questions, some known results, many applications, mathematical properties, a variety of numerical techniques, as well as several open problems. This is the first book in the authoritative Numerical Mathematics and Scientific Computation series to cover numerical linear algebra, a broad area of numerical analysis. Authored by two world-renowned researchers, the book is aimed at graduates and researchers in applied mathematics, engineering and computer science and makes an ideal graduate text.
Fixed Point Algorithms For Inverse Problems In Science And Engineering
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Author : Heinz H. Bauschke
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-27
Fixed Point Algorithms For Inverse Problems In Science And Engineering written by Heinz H. Bauschke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-27 with Mathematics categories.
"Fixed-Point Algorithms for Inverse Problems in Science and Engineering" presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems. This book incorporates diverse perspectives from broad-ranging areas of research including, variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics, and chemistry. Topics presented include: Theory of Fixed-point algorithms: convex analysis, convex optimization, subdifferential calculus, nonsmooth analysis, proximal point methods, projection methods, resolvent and related fixed-point theoretic methods, and monotone operator theory. Numerical analysis of fixed-point algorithms: choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of ill-posed problems; numerical comparison of various methods. Areas of Applications: engineering (image and signal reconstruction and decompression problems), computer tomography and radiation treatment planning (convex feasibility problems), astronomy (adaptive optics), crystallography (molecular structure reconstruction), computational chemistry (molecular structure simulation) and other areas. Because of the variety of applications presented, this book can easily serve as a basis for new and innovated research and collaboration.
Proximal Algorithms
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Author : Neal Parikh
language : en
Publisher: Now Pub
Release Date : 2013-11
Proximal Algorithms written by Neal Parikh and has been published by Now Pub this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11 with Mathematics categories.
Proximal Algorithms discusses proximal operators and proximal algorithms, and illustrates their applicability to standard and distributed convex optimization in general and many applications of recent interest in particular. Much like Newton's method is a standard tool for solving unconstrained smooth optimization problems of modest size, proximal algorithms can be viewed as an analogous tool for nonsmooth, constrained, large-scale, or distributed versions of these problems. They are very generally applicable, but are especially well-suited to problems of substantial recent interest involving large or high-dimensional datasets. Proximal methods sit at a higher level of abstraction than classical algorithms like Newton's method: the base operation is evaluating the proximal operator of a function, which itself involves solving a small convex optimization problem. These subproblems, which generalize the problem of projecting a point onto a convex set, often admit closed-form solutions or can be solved very quickly with standard or simple specialized methods. Proximal Algorithms discusses different interpretations of proximal operators and algorithms, looks at their connections to many other topics in optimization and applied mathematics, surveys some popular algorithms, and provides a large number of examples of proximal operators that commonly arise in practice.
Nanoscale Photonic Imaging
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Author : Tim Salditt
language : en
Publisher: Springer Nature
Release Date : 2020-06-09
Nanoscale Photonic Imaging written by Tim Salditt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-09 with Science categories.
This open access book, edited and authored by a team of world-leading researchers, provides a broad overview of advanced photonic methods for nanoscale visualization, as well as describing a range of fascinating in-depth studies. Introductory chapters cover the most relevant physics and basic methods that young researchers need to master in order to work effectively in the field of nanoscale photonic imaging, from physical first principles, to instrumentation, to mathematical foundations of imaging and data analysis. Subsequent chapters demonstrate how these cutting edge methods are applied to a variety of systems, including complex fluids and biomolecular systems, for visualizing their structure and dynamics, in space and on timescales extending over many orders of magnitude down to the femtosecond range. Progress in nanoscale photonic imaging in Göttingen has been the sum total of more than a decade of work by a wide range of scientists and mathematicians across disciplines, working together in a vibrant collaboration of a kind rarely matched. This volume presents the highlights of their research achievements and serves as a record of the unique and remarkable constellation of contributors, as well as looking ahead at the future prospects in this field. It will serve not only as a useful reference for experienced researchers but also as a valuable point of entry for newcomers.