Rank-k modification methods for recursive least squares problems

Olszanskyj, S.J.; Lebak, James; Bojańczyk, Adam W.

doi:10.1007/bf02140689

Cited by 20 publications

(7 citation statements)

References 14 publications

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“…Several methods have been proposed to solve the up-and down-dating least-squares problem [11,21,27,32,39,50,51,59,93,98,105,108,114,115,144]. Parallel strategies for solving the up-and down-dating OLM problem will be considered.…”

Section: Discussionmentioning

confidence: 99%

“…If the original matrix W is available, then the downdated SEM can be solved afresh or the matrix that corresponds to R in (6.7) can be derived from downdating the incomplete QRD of W [39,50,51,75,108,109]. However, as in the updating problem, the solution of the downdated TSEM will have to be recomputed from scratch.…”

Section: R(3) T 'mentioning

confidence: 99%

“…Givens sequence, 160 set of matrices, 29, 34 structured banded matrices, 82 bitonic method,82 illustration,82,85 updating,58,67,72,84 weighted,8 Rank,3,[5][6][9][10]87 criterion,41 full column,40,57,121,147,149 not full,39 Recurrence,145 Recursive doubling,67 Regression,1,117 model,41 stepwise,42,48,61,127 Residuals,1,3,5,62,120 Set of vectors notation,118 SIMD,[17][18]73,108 arrays , Subject Index 181 DAP,24,[40][41]48,52,…”

Section: Subject Indexmentioning

confidence: 99%

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Parallel Algorithms for Linear Models

Kontoghiorghes¹

2000

Advances in Computational Economics

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Section: Discussionmentioning

confidence: 99%

Section: R(3) T 'mentioning

confidence: 99%

Section: Subject Indexmentioning

confidence: 99%

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Parallel Algorithms for Linear Models

Kontoghiorghes¹

2000

Advances in Computational Economics

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“…New and modified algorithms based on coarse-grained, systolic and other realworld programming models should be proposed [3], [7], [26], [27], [37], [38]. Recent advances made in the design of block-parallel matrix algorithms and portable numerical libraries and tools that facilitate the efficient implementation of parallel matrix algorithms should be taken into consideration [1], [4], [9], [10], [30], [32].…”

Section: Conclusion and Futurementioning

confidence: 99%

Parallel Strategies for Computing the Orthogonal Factorizations Used in the Estimation of Econometric Models

Kontoghiorghes

1999

Algorithmica

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Parallel strategies based on compound disjoint Givens rotations are proposed for computing the main two factorizations that are used in the solution of seemingly unrelated regression and simultaneous equations models. The first factorization requires the triangularization of a set of upper-trapezoidals after deleting columns. The second factorization is equivalent to updating a lower-triangular matrix with a matrix having a block lower-triangular structure. Theoretical measures of complexity and examples are used for comparing and investigating the various parallel strategies. 1. Introduction. The estimation of simultaneous equations models (SEMs) is of great importance in econometric and financial modeling [13], [37]. The most commonly used estimation procedures are the Three Stage Least-Squares (3SLS) and the computationally expensive maximum likelihood [8], [12], [31], [33], [39]. Recently, new computational and numerical methods which substantially reduce the computational burden of deriving the 3SLS solution of SEMs have been proposed [2], [25]. These methods have, as a basic component, the QR decomposition (QRD) and its modification. The goal of this work is to provide theoretically-based efficient parallel strategies for computing these decompositions using as few steps as possible. These strategies will form the basis for implementing the new 3SLS and the simplified SURE model estimation algorithms on parallel systems [16], [20], [23].The SEM can be written in the form

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“…The orthogonal matrix Q 2 and the upper triangular matrix R 2 in (6) are of order (m − d) and n, respectively. Different sequential strategies for solving the downdating least squares problem have been proposed [3,[8][9][10][12][13][14]. These mainly consider Givens rotations for downdating the LS solution by single observation, or the straightforward use of the QRD for downdating the block of observations.…”

Section: Introductionmentioning

confidence: 99%