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Tables of Contents for Parallel Algorithms for Linear Models
Chapter/Section Title
Page #
Page Count
List of Figures
ix
List of Tables
xi
List of Algorithms
xiii
Preface
xv
Linear Models and Qr Decomposition
1
38
Introduction
1
1
Linear model specification
1
9
The ordinary linear model
2
5
The general linear model
7
3
Forming the QR decomposition
10
7
The Householder method
11
2
The Givens rotation method
13
3
The Gram-Schmidt orthogonalization method
16
1
Data parallel algorithms for computing the QR decomposition
17
6
Data parallelism and the MasPar SIMD system
17
2
The Householder method
19
2
The Gram-Schmidt method
21
1
The Givens roatation method
22
1
Computational results
23
1
QRD of large and skinny matrices
23
6
The CPP GAMMA SIMD system
24
1
The Householder QRD algorithm
25
2
QRD of skinny matrices
27
2
QRD of a set of matrices
29
10
Equal size matrices
29
5
Matrices with different number of columns
34
5
Olm Not of Full Rank
39
18
Introduction
39
1
The QLD of the coefficient matrix
40
3
SIMD implementation
41
2
Triangularizing the lower trapezoid
43
6
The Householder method
43
3
The Givens method
46
3
Computing the orthogonal matrices
49
5
Discussion
54
3
Updating and Downdating the Olm
57
48
Introduction
57
1
Adding observations
58
32
The hybrid Householder algorithm
60
7
The Bitonic and Greedy Givens sequences
67
8
Updating with a block lower-triangular matrix
75
7
QRD of structured banded matrices
82
5
Recursive and linearly constrained least-squares
87
3
Adding exogenous varibales
90
2
Deleting observations
92
7
Parallel strategies
94
5
Deleting exogenous variables
99
6
The General Linear Model
105
12
Introduction
105
3
Parallel algorithms
108
3
Implementation and performance analysis
111
6
Sure Models
117
30
Introduction
117
4
The generalized linear least squares method
121
2
Triangular SURE models
123
6
Implementation aspects
127
2
Covariance restrictions
129
18
The QLD of the block bi-diagonal matrix
133
5
Parallel strategies
138
2
Common exogenous variables
140
7
Simultaneous Equations Models
147
16
Generalized linear least squares
149
5
Estimating the disturbance covariance matrix
151
1
Redundancies
152
1
Inconsistencies
153
1
Modifying the SEM
154
3
Linear Equality Constraints
157
3
Basis of the null space and direct elimination methods
158
2
Computational Strategies
160
3
References
163
14
Author Index
177
2
Subject Index
179