## Linear Least Squares ComputationsPresenting numerous algorithms in a simple algebraic form so that the reader can easily translate them into any computer language, this volume gives details of several methods for obtaining accurate least squares estimates. It explains how these estimates may be updated as new information becomes available and how to test linear hypotheses. Linear Least Squares Computations features many structured exercises that guide the reader through the available algorithms, plus a glossary of commonly used terms and a bibliography of supplementary reading ... collects "ancient" and modern results on linear least squares computations in a convenient single source ... develops the necessary matrix algebra in the context of multivariate statistics ... only makes peripheral use of concepts such as eigenvalues and partial differentiation ... interprets canonical forms employed in computation ... discusses many variants of the Gauss, Laplace-Schmidt, Givens, and Householder algorithms ... and uses an empirical approach for the appraisal of algorithms. Linear Least Squares Computations serves as an outstanding reference for industrial and applied mathematicians, statisticians, and econometricians, as well as a text for advanced undergraduate and graduate statistics, mathematics, and econometrics courses in computer programming, linear regression analysis, and applied statistics. Book jacket. |

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### Contents

THE GAUSS AND GAUSSJORDAN | 1 |

THE CAUCHYBIENAYME LAPLACE | 59 |

Procedures | 69 |

Contents | 81 |

GIVENSS PROCEDURE | 97 |

UPDATING THE QU DECOMPOSITION | 127 |

PSEUDORANDOM NUMBERS | 141 |

THE STANDARD LINEAR MODEL | 153 |

GENERALIZED LEAST SQUARES | 185 |

Givens Transformations II | 201 |

ITERATIVE SOLUTIONS OF LINEAR | 217 |

CANONICAL EXPRESSIONS FOR THE LEAST | 229 |

TRADITIONAL EXPRESSIONS FOR | 245 |

Contents xiii | 257 |

275 | |

283 | |

### Common terms and phrases

accuracy algebraic algorithm of Sec backsubstitution Cauchy Cauchy-Bienayme procedure Cholesky decomposition columns constraints context defined delete diagonal elements empirical condition number equations expressions Gauss-Jordan Gauss's method Gauss's procedure Givens transformation Givens's procedure Householder transformation Householder's procedure instrumental variable estimator integers Laplace Laplace's procedure least squares estimator Least Squares Problems limit condition number Linear Least Squares lower triangular matrix m x p matrix satisfying method of Sec multiplications n x n orthonormal matrix n x p matrix nonsingular matrix nonzero normally distributed observations obtain orthogonalization procedure permutation positive definite positive semidefinite positive semidefinite matrix premultiplying program of Exercise pseudo-random numbers real numbers Regression Reprinted solution squares residuals standard linear model Stat Statistical subtract sum of squared symmetric matrix third row unbiased estimator upper triangular form upper triangular matrix var(P variance matrix weighted least squares Write a program