### Petko Yanev (Université de Neuchâtel, Switzerland)

#### Numerical algorithms for estimating least squares problems

*ERGO Optimization day: Thursday 18 August 2005 at 15.00, JCMB 5327*

##### Abstract

The solution of least squares estimation problems is of great
importance in the areas of numerical linear algebra, computational
statistics and econometrics. The design and analysis of numerically
stable and computationally efficient methods for solving such least
squares problems is considered. The main computational tool used for
the estimation of the least squares solutions is the QR decomposition,
or the generalized QR decomposition. Specifically, emphasis is given
to the design of sequential and parallel strategies for computing the
main matrix factorizations which arise in the estimation procedures.
The strategies are based on block-generalizations of the Givens
sequences and efficiently exploit the structure of the matrices.

- An efficient minimum spanning tree algorithm is proposed for computing
the QR decomposition of a set of matrices which have common columns.
Heuristic strategies are also considered.
- Several computationally efficient sequential algorithms for block
downdating of the least squares solutions are discussed in details.
A parallel algorithm based on the best sequential approach
for downdating the QR decomposition is also proposed.
- Within the context of block up-downdating, efficient serial and parallel
algorithms for computing the estimators of the general linear model (GLM) and
seemingly unrelated regression models (SUR) after been updated with new
observations are proposed.

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