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Numerical Methods for Least Squares Problems

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The method of least squares was discovered by Gauss in 1795. It has since become the principal tool for reducing 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.

About the Author

Ake Bjorck is Professor of Mathematics at Linkoping University in Sweden. He has coauthored the wellknown textbook Numerical Methods with Germund Dahlquist and has published more than 50 technical papers. He is the managing editor of BIT and has served on the editorial boards of many other prominent international journals. He has been a member of SIAM since 1969.

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