Bjorck A. Numerical Methods for Least Squares Problems 2ed 2024

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Bjorck A. Numerical Methods for Least Squares Problems 2ed 2024

Textbook in PDF format The method of least squares, discovered by Gauss in 1795, is a principal tool for reducing the influence of errors when fitting a mathematical model to given observations. Applications arise in many areas of science and engineering. The increased use of automatic data capturing frequently leads to large-scale least squares problems. Such problems can be solved by using recent developments in preconditioned iterative methods and in sparse QR factorization. The first edition of Numerical Methods for Least Squares Problems was the leading reference on the topic for many years. The updated second edition stands out compared to other books on this subject because it provides an in-depth and up-to-date treatment of direct and iterative methods for solving different types of least squares problems and for computing the singular value decomposition. It also is unique because it covers generalized, constrained, and nonlinear least squares problems as well as partial least squares and regularization methods for discrete ill-posed problems. The bibliography of over 1,100 historical and recent references provides a comprehensive survey of past and present research in the field. List of Figures. List of Tables. Preface. Preface to the First Edition. Mathematical and Statistical Foundations. Basic Numerical Methods. Generalized and Constrained Least Squares. Special Least Squares Problems. Direct Methods for Sparse Problems. Iterative Methods. SVD Algorithms and Matrix Functions. Bibliography. Index