## Numerical Methods for Least Squares ProblemsThe method of least squares was discovered by Gauss in 1795 and 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 and tremendous progress has been made in numerical methods for least squares 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. |

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The Best available resource on the least squares technique...

both theory and applications.

### Contents

Basic Numerical Methods | 37 |

Modified Least Squares Problems | 127 |

Generalized Least Squares Problems | 153 |

Constrained Least Squares Problems | 187 |

Direct Methods for Sparse Problems | 215 |

Iterative Methods For Least Squares Problems | 269 |

### Common terms and phrases

applied approximation assume backward stable bidiagonal Bjorck block bounds Chebyshev Cholesky factor column pivoting compute the QR condition number consider constraints convergence corresponding deleting denotes determined diagonal elements downdating eigenvalues error analysis estimate example flops follows function Gauss-Newton method Givens rotations Golub graph GSVD Hence Householder transformations ill-conditioned implementation iterative methods iterative refinement least squares problem least squares solution linear least squares linear systems method of normal minimize minimum norm multifrontal nodes nonlinear least squares nonsingular nonzero elements normal equations Note nullspace obtained optimal orthogonal orthogonal matrix parameter permutation matrix perturbation polynomials positive definite preconditioner problem LSE pseudoinverse QR algorithm QR decomposition R"xn rank deficient rank revealing reduced requires residual Rmxn satisfies scheme Section sequence singular value decomposition singular vectors sparse matrix step storage structure subspace Theorem TLS problem triangular form triangular matrix updating upper triangular variables zero