## Linear Least Squares ComputationsPresenting numerous algorithms in a simple algebraic form so that the reader can easilytranslate them into any computer language, this volume gives details of several methodsfor obtaining accurate least squares estimates. It explains how these estimates may beupdated as new information becomes available and how to test linear hypotheses.Linear Least Squares Computations features many structured exercises that guidethe reader through the available algorithms, plus a glossary of commonly used terms anda bibliography of supplementary reading ... collects "ancient" and modem results onlinear least squares computations in a convenient single source . . . develops the necessarymatrix algebra in the context of multivariate statistics . .. only makes peripheral use ofconcepts such as eigenvalues and partial differentiation .. . interprets canonical formsemployed in computation ... discusses many variants of the Gauss, Laplace-Schmidt, Givens, and Householder algorithms ... and uses an empirical approach for the appraisalof algorithms.Linear Least Squares Computations serves as an outstanding reference forindustrial and applied mathematicians, statisticians, and econometricians, as well as atext for advanced undergraduate and graduate statistics, mathematics, and econometricscourses in computer programming, linear regression analysis, and applied statistics |

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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 | |

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### 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