Preconditioning Linear Least-Squares Problems by Identifying a Basis Matrix

Preconditioning of linear least-squares problems by identifying basic variables

The preconditioning of linear least-squares problems is a hard task. The linear model underpinning least-squares problems, that is the overdetermined matrix defining it, does not have the properties of differential problems that make standard preconditioners effective. Incomplete Cholesky techniques applied to the normal equations do not produce a well conditioned problem. We attempt to remove ...

Linear Least Squares Problems

A fundamental task in scientific computing is to estimate parameters in a mathematical model from collected data which are subject to errors. The influence of the errors can be reduced by using a greater number of data than the number of unknowns. If the model is linear, the resulting problem is then to “solve” an in general inconsistent linear system Ax = b, where A ∈ Rm×n and m ≥ n. In other ...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

Greville's method for preconditioning least squares problems

X. Cui Department of Informatics, School of Multidisciplinary Sciences, The Graduate University for Advanced Studies (Sokendai), 2-1-2, Hitotsubashi, Chiyoda-ku, Tokyo, Japan, 101-8430 K. Hayami Principles of Informatics Research Division, National Institute of Informatics, 2-1-2, Hitotsubashi, Chiyodaku, Tokyo, Japan, 101-8430 J. Yin Department of Mathematics, Tongji University, Shanghai, P.R....

least squares solutions of inconsistent fuzzy linear matrix equations

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