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Supremum And Stability Of Weighted Pseudoinverses And Weighted Least Squares Problems Analysis And Computations
Download Supremum And Stability Of Weighted Pseudoinverses And Weighted Least Squares Problems Analysis And Computations full books in PDF, epub, and Kindle. Read online Supremum And Stability Of Weighted Pseudoinverses And Weighted Least Squares Problems Analysis And Computations ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Supremum and Stability of Weighted Pseudoinverses and Weighted Least Squares Problems Analysis and Computations by : Musheng Wei
Download or read book Supremum and Stability of Weighted Pseudoinverses and Weighted Least Squares Problems Analysis and Computations written by Musheng Wei and published by Nova Biomedical Books. This book was released on 2001 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rapid development of computing power of personal computers, workstations, mainframes, super computers and integrated circuits has provided scientists and engineers with powerful tools in solving their scientific problems using computers, and is expected to continue to increase well in the future. The monograph mainly contains the following three parts: analysis of supremum of weighted pseudoinverses, study the stability of weighted pseudoinverses, weighted least squares problems and constrained weighted least squares problems, and stable methods for solving weighted least squares problems and constrained weighted least squares problems.
Book Synopsis Generalized Inverses: Theory and Computations by : Guorong Wang
Download or read book Generalized Inverses: Theory and Computations written by Guorong Wang and published by Springer. This book was released on 2018-05-12 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book begins with the fundamentals of the generalized inverses, then moves to more advanced topics. It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the generalized inverses, perturbation analysis of the generalized inverses, an algorithmic study of the computational methods for the full-rank factorization of a generalized inverse, generalized singular value decomposition, imbedding method, finite method, generalized inverses of polynomial matrices, and generalized inverses of linear operators. This book is intended for researchers, postdocs, and graduate students in the area of the generalized inverses with an undergraduate-level understanding of linear algebra.
Book Synopsis Handbook of Linear Algebra by : Leslie Hogben
Download or read book Handbook of Linear Algebra written by Leslie Hogben and published by CRC Press. This book was released on 2013-11-26 with total page 1838 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and
Book Synopsis Applications of Linear and Nonlinear Models by : Erik Grafarend
Download or read book Applications of Linear and Nonlinear Models written by Erik Grafarend and published by Springer Science & Business Media. This book was released on 2012-08-15 with total page 1026 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear regression models within the first 8 chapters. Our point of view is both an algebraic view as well as a stochastic one. For example, there is an equivalent lemma between a best, linear uniformly unbiased estimation (BLUUE) in a Gauss-Markov model and a least squares solution (LESS) in a system of linear equations. While BLUUE is a stochastic regression model, LESS is an algebraic solution. In the first six chapters we concentrate on underdetermined and overdeterimined linear systems as well as systems with a datum defect. We review estimators/algebraic solutions of type MINOLESS, BLIMBE, BLUMBE, BLUUE, BIQUE, BLE, BIQUE and Total Least Squares. The highlight is the simultaneous determination of the first moment and the second central moment of a probability distribution in an inhomogeneous multilinear estimation by the so called E-D correspondence as well as its Bayes design. In addition, we discuss continuous networks versus discrete networks, use of Grassmann-Pluecker coordinates, criterion matrices of type Taylor-Karman as well as FUZZY sets. Chapter seven is a speciality in the treatment of an overdetermined system of nonlinear equations on curved manifolds. The von Mises-Fisher distribution is characteristic for circular or (hyper) spherical data. Our last chapter eight is devoted to probabilistic regression, the special Gauss-Markov model with random effects leading to estimators of type BLIP and VIP including Bayesian estimation. A great part of the work is presented in four Appendices. Appendix A is a treatment, of tensor algebra, namely linear algebra, matrix algebra and multilinear algebra. Appendix B is devoted to sampling distributions and their use in terms of confidence intervals and confidence regions. Appendix C reviews the elementary notions of statistics, namely random events and stochastic processes. Appendix D introduces the basics of Groebner basis algebra, its careful definition, the Buchberger Algorithm, especially the C. F. Gauss combinatorial algorithm.
Book Synopsis Matrix Theory by : Mykhaylo Andriychuk
Download or read book Matrix Theory written by Mykhaylo Andriychuk and published by BoD – Books on Demand. This book was released on 2023 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix Theory - Classics and Advances examines matrix theory and its application in solving a series of problems related to natural phenomena and applied science. It consists of eleven chapters divided into two sections. Section 1, "Theory and Progress", discusses the classical problems of matrix theory and its contribution to different fields of pure mathematics. Section 2, "Applications", contains the research related to the application of matrix theory in applied science.
Book Synopsis Applications of Linear and Nonlinear Models by : Erik W. Grafarend
Download or read book Applications of Linear and Nonlinear Models written by Erik W. Grafarend and published by Springer Nature. This book was released on 2022-10-01 with total page 1127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides numerous examples of linear and nonlinear model applications. Here, we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear regression models within the first 8 chapters. Our point of view is both an algebraic view and a stochastic one. For example, there is an equivalent lemma between a best, linear uniformly unbiased estimation (BLUUE) in a Gauss–Markov model and a least squares solution (LESS) in a system of linear equations. While BLUUE is a stochastic regression model, LESS is an algebraic solution. In the first six chapters, we concentrate on underdetermined and overdetermined linear systems as well as systems with a datum defect. We review estimators/algebraic solutions of type MINOLESS, BLIMBE, BLUMBE, BLUUE, BIQUE, BLE, BIQUE, and total least squares. The highlight is the simultaneous determination of the first moment and the second central moment of a probability distribution in an inhomogeneous multilinear estimation by the so-called E-D correspondence as well as its Bayes design. In addition, we discuss continuous networks versus discrete networks, use of Grassmann–Plucker coordinates, criterion matrices of type Taylor–Karman as well as FUZZY sets. Chapter seven is a speciality in the treatment of an overjet. This second edition adds three new chapters: (1) Chapter on integer least squares that covers (i) model for positioning as a mixed integer linear model which includes integer parameters. (ii) The general integer least squares problem is formulated, and the optimality of the least squares solution is shown. (iii) The relation to the closest vector problem is considered, and the notion of reduced lattice basis is introduced. (iv) The famous LLL algorithm for generating a Lovasz reduced basis is explained. (2) Bayes methods that covers (i) general principle of Bayesian modeling. Explain the notion of prior distribution and posterior distribution. Choose the pragmatic approach for exploring the advantages of iterative Bayesian calculations and hierarchical modeling. (ii) Present the Bayes methods for linear models with normal distributed errors, including noninformative priors, conjugate priors, normal gamma distributions and (iii) short outview to modern application of Bayesian modeling. Useful in case of nonlinear models or linear models with no normal distribution: Monte Carlo (MC), Markov chain Monte Carlo (MCMC), approximative Bayesian computation (ABC) methods. (3) Error-in-variables models, which cover: (i) Introduce the error-in-variables (EIV) model, discuss the difference to least squares estimators (LSE), (ii) calculate the total least squares (TLS) estimator. Summarize the properties of TLS, (iii) explain the idea of simulation extrapolation (SIMEX) estimators, (iv) introduce the symmetrized SIMEX (SYMEX) estimator and its relation to TLS, and (v) short outview to nonlinear EIV models. The chapter on algebraic solution of nonlinear system of equations has also been updated in line with the new emerging field of hybrid numeric-symbolic solutions to systems of nonlinear equations, ermined system of nonlinear equations on curved manifolds. The von Mises–Fisher distribution is characteristic for circular or (hyper) spherical data. Our last chapter is devoted to probabilistic regression, the special Gauss–Markov model with random effects leading to estimators of type BLIP and VIP including Bayesian estimation. A great part of the work is presented in four appendices. Appendix A is a treatment, of tensor algebra, namely linear algebra, matrix algebra, and multilinear algebra. Appendix B is devoted to sampling distributions and their use in terms of confidence intervals and confidence regions. Appendix C reviews the elementary notions of statistics, namely random events and stochastic processes. Appendix D introduces the basics of Groebner basis algebra, its careful definition, the Buchberger algorithm, especially the C. F. Gauss combinatorial algorithm.
Book Synopsis Numerical Methods for Least Squares Problems by : Ake Bjorck
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.
Book Synopsis Linear Algebra Research Advances by : Gerald D. Ling
Download or read book Linear Algebra Research Advances written by Gerald D. Ling and published by . This book was released on 2007 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear maps (also called linear transformations), and systems of linear equations. Vector spaces are a central theme in modern mathematics; thus, linear algebra is widely used in both abstract algebra and functional analysis. Linear algebra also has a concrete representation in analytic geometry and it is generalised in operator theory. It has extensive applications in the natural sciences and the social sciences, since non-linear models can often be approximated by linear ones.
Book Synopsis Weighted Least Squares Perturbation Theory by : Elena Nikolaevskaya
Download or read book Weighted Least Squares Perturbation Theory written by Elena Nikolaevskaya and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interest in the problem of weighted pseudoinverse matrices and the problem of weighted least squares (WLS) is largely due to their numerous applications. In particular, the problem of WLS is used in the design and optimization of building structures, in tomography, in statistics, etc. The first part of the chapter is devoted to the sensitivity of the solution to the WLS problem with approximate initial data. The second part investigates the properties of a SLAE with approximate initial data and presents an algorithm for finding a weighted normal pseudo solution of a WLS problem with approximate initial data, an algorithm for solving a WLS problem with symmetric positive semidefinite matrices and an approximate right side and also a parallel algorithm for solving a WLS problem. The third part is devoted to the analysis of the reliability of computer solutions of the WLS problem with approximate initial data. Here, estimates of the total error of the WLS problem are presented, and also software-algorithmic approaches to improving the accuracy of computer solutions.
Book Synopsis Stable and Efficient Solution of Weighted Least-squares Problems with Applications in Interior Point Methods by : Patricia D. Hough
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:
Book Synopsis Linear Least Squares Computations by : Farebrother
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 Bibliographic Index written by and published by . This book was released on 2001 with total page 1110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Book Review Index written by and published by . This book was released on 2002 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stability of Algorithms for Solving Weighted and Constrained Least Squares Problems by : Anthony James Cox
Download or read book Stability of Algorithms for Solving Weighted and Constrained Least Squares Problems written by Anthony James Cox and published by . This book was released on 1997 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis American Book Publishing Record by :
Download or read book American Book Publishing Record written by and published by . This book was released on 2001 with total page 2744 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Applied Linear Algebra by : Stephen Boyd
Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
