Incomplete Factorization Preconditioning For Linear Least Squares Problems
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Incomplete Factorization Preconditioning for Linear Least Squares Problems
When certain conditions are imposed on the sparsity pattern of the preconditioning matrix, incomplete Cholesky (IC) factorization is identical to IMGS. Therefore, a sufficient condition on the sparsity pattern for a stable IC factorization can be derived. Based on this condition, three algorithms for modifying a sparsity pattern for which IC may not succeed have been designed. These methods differ from previously proposed methods to guarantee the existence and improve the stability of the IC factorization since they do not require numerical information. Numerical experiments illustrating the capabilities of the preconditioners are also presented."
Numerical Methods for Least Squares Problems
The method of least squares: the principal tool for reducing the influence of errors when fitting models to given observations.
Numerical Methods for Least Squares Problems, Second Edition
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. This book will be of interest to graduate students and researchers in applied mathematics and to researchers working with numerical linear algebra applications.