Download or read book An Extension of Kaczmarz s Projections Method with Relaxation Parameter to 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 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Iterative Methods for Fixed Point Problems in Hilbert Spaces written by Andrzej Cegielski and published by Springer. This book was released on 2012-09-14 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative methods for finding fixed points of non-expansive operators in Hilbert spaces have been described in many publications. In this monograph we try to present the methods in a consolidated way. We introduce several classes of operators, examine their properties, define iterative methods generated by operators from these classes and present general convergence theorems. On this basis we discuss the conditions under which particular methods converge. A large part of the results presented in this monograph can be found in various forms in the literature (although several results presented here are new). We have tried, however, to show that the convergence of a large class of iteration methods follows from general properties of some classes of operators and from some general convergence theorems.
Download or read book Parallelism in Matrix Computations written by Efstratios Gallopoulos and published by Springer. This book was released on 2015-07-25 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations. It assumes general but not extensive knowledge of numerical linear algebra, parallel architectures, and parallel programming paradigms. The book consists of four parts: (I) Basics; (II) Dense and Special Matrix Computations; (III) Sparse Matrix Computations; and (IV) Matrix functions and characteristics. Part I deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Part II is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singular-value decomposition. It also deals with the development of parallel algorithms for special linear systems such as banded ,Vandermonde ,Toeplitz ,and block Toeplitz systems. Part III addresses sparse matrix computations: (a) the development of parallel iterative linear system solvers with emphasis on scalable preconditioners, (b) parallel schemes for obtaining a few of the extreme eigenpairs or those contained in a given interval in the spectrum of a standard or generalized symmetric eigenvalue problem, and (c) parallel methods for computing a few of the extreme singular triplets. Part IV focuses on the development of parallel algorithms for matrix functions and special characteristics such as the matrix pseudospectrum and the determinant. The book also reviews the theoretical and practical background necessary when designing these algorithms and includes an extensive bibliography that will be useful to researchers and students alike. The book brings together many existing algorithms for the fundamental matrix computations that have a proven track record of efficient implementation in terms of data locality and data transfer on state-of-the-art systems, as well as several algorithms that are presented for the first time, focusing on the opportunities for parallelism and algorithm robustness.
Download or read book Characterization of the Solutions Set of Least squares Problems by an Extension of Kaczmarz s Projections Methods written by Constantin Popa and published by . This book was released on 1997 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We give a new characterization of the solutions set of the general (inconsistent) linear least-squares problem using the set of limit-points of an extended version of the classical Kaczmarz's projections method. We also obtain a 'step error reduction formula' which, at least from a theoretical view point, can give us information about the convergence properties of the algorithm. In section 3 we present a modified version of the above extended algorithm, obtained by a class of nonorthogonal transformations of the initial least-squares problem and we prove for it similar results as for the initial one. Some comparisons concerning computational aspects, between our algorithms and others existent in the literature, are made in the last section of the paper."
Download or read book Mathematical Reviews written by and published by . This book was released on 2000 with total page 844 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Radioengineering written by and published by . This book was released on 2008 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 BIT written by and published by . This book was released on 1998 with total page 844 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Successive Overrelaxation Methods for Solving Large Scale Rank Deficient Least Squares Problems written by Valerie A. Miller and published by . This book was released on 1985 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Iterative Methods written by Charles L. Byrne and published by A K Peters/CRC Press. This book was released on 2008 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of essays on iterative algorithms and their uses. It focuses on the mathematics of medical image reconstruction, with emphasis on Fourier inversion. The book discusses the problems and algorithms in the context of operators on finite-dimensional Euclidean space.
Download or read book Iterative Optimization in Inverse Problems written by Charles Byrne and published by CRC Press. This book was released on 2014-02-12 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative Optimization in Inverse Problems brings together a number of important iterative algorithms for medical imaging, optimization, and statistical estimation. It incorporates recent work that has not appeared in other books and draws on the author's considerable research in the field, including his recently developed class of SUMMA algorithms
Download or read book Parallel Optimization written by Yair Censor and published by Oxford University Press, USA. This book was released on 1997 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a unique pathway to methods of parallel optimization by introducing parallel computing ideas into both optimization theory and into some numerical algorithms for large-scale optimization problems. The three parts of the book bring together relevant theory, careful study of algorithms, and modeling of significant real world problems such as image reconstruction, radiation therapy treatment planning, financial planning, transportation and multi-commodity network flow problems, planning under uncertainty, and matrix balancing problems.
Download or read book Characterization of the Solutions Set of Least squares Problems by an Extension of Kacmarz s Projections Methods written by Constantin Popa and published by . This book was released on 1997 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Iterative Krylov Methods for Large Linear Systems written by H. A. van der Vorst and published by Cambridge University Press. This book was released on 2003-04-17 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
Download or read book Generalized Inverses written by Adi Ben-Israel and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition accounts for many major developments in generalized inverses while maintaining the informal and leisurely style of the 1974 first edition. Added material includes a chapter on applications, new exercises, and an appendix on the work of E.H. Moore.
Download or read book Numerical Methods for Least Squares Problems written by Ake Bjorck and published by SIAM. This book was released on 1996-01-01 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of least squares was discovered by Gauss in 1795. It has since become the principal tool to reduce the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing. Least squares problems of large size are now routinely solved. Tremendous progress has been made in numerical methods for least squares problems, in particular for generalized and modified least squares problems and direct and iterative methods for sparse problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject.
Download or read book Projections and Approximate Orthogonalization for Numerical Solution of Inconsistent Least squares Problems written by Constantin Popa and published by . This book was released on 1999 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
