Parallel Algorithms for Linear Models

Parallel Algorithms for Linear Models provides a complete and detailed account of the design, analysis and implementation of parallel algorithms for solving large-scale linear models. It investigates and presents efficient, numerically stable algorithms for computing the least-squares estimators and other quantities of interest on massively parallel systems.
The monograph is in two parts. The first part consists of four chapters and deals with the computational aspects for solving linear models that have applicability in diverse areas. The remaining two chapters form the second part, which concentrates on numerical and computational methods for solving various problems associated with seemingly unrelated regression equations (SURE) and simultaneous equations models.
The practical issues of the parallel algorithms and the theoretical aspects of the numerical methods will be of interest to a broad range of researchers working in the areas of numerical and computational methods in statistics and econometrics, parallel numerical algorithms, parallel computing and numerical linear algebra. The aim of this monograph is to promote research in the interface of econometrics, computational statistics, numerical linear algebra and parallelism.

Klappentext

Parallel Algorithms for Linear Models provides a complete and detailed account of the design, analysis and implementation of parallel algorithms for solving large-scale linear models. It investigates and presents efficient, numerically stable algorithms for computing the least-squares estimators and other quantities of interest on massively parallel systems. The monograph is in two parts. The first part consists of four chapters and deals with the computational aspects for solving linear models that have applicability in diverse areas. The remaining two chapters form the second part, which concentrates on numerical and computational methods for solving various problems associated with seemingly unrelated regression equations (SURE) and simultaneous equations models. The practical issues of the parallel algorithms and the theoretical aspects of the numerical methods will be of interest to a broad range of researchers working in the areas of numerical and computational methods in statistics and econometrics, parallel numerical algorithms, parallel computing and numerical linear algebra. The aim of this monograph is to promote research in the interface of econometrics, computational statistics, numerical linear algebra and parallelism.

Inhalt

1. Linear Models and QR Decomposition.- 1 Introduction.- 2 Linear model specification.- 3 Forming the QR decomposition.- 4 Data parallel algorithms for computing the QR decomposition.- 5 QRD of large and skinny matrices.- 6 QRD of a set of matrices.- 2. Olm Not of Full Rank.- 1 Introduction.- 2 The QLD of the coefficient matrix.- 3 Triangularizing the lower trapezoid.- 4 Computing the orthogonal matrices.- 5 Discussion.- 3. Updating and Downdating The Olm.- 1 Introduction.- 2 Adding observations.- 3 Adding exogenous variables.- 4 Deleting observations.- 5 Deleting exogenous variables.- 4. The General Linear Model.- 1 Introduction.- 2 Parallel algorithms.- 3 Implementation and performance analysis.- 5. Sure Models.- 1 Introduction.- 2 The generalized linear least squares method.- 3 Triangular SURE models.- 4 Covariance restrictions.- 6. Simultaneous Equations Models.- 1 Generalized linear least squares.- 2 Modifying the SEM.- 3 Linear Equality Constraints.- 4 Computational Strategies.- References.- Author Index.