Accurate Downdating of Least Squares Solutions

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

Parallel algorithms for downdating the least squares estimator of the regression model

Computationally efficient parallel algorithms for downdating the least squares estimator of the ordinary linear regression are proposed. The algorithms, which are based on the QR decomposition, are block versions of sequential Givens strategies and efficiently exploit the triangular structure of the data matrices. The first strategy utilizes only part of the orthogonal matrix which is derived f...

Least squares solutions of bilinear equations

In this second recitation, we will address the following topics: • Review of the projection theorem. • Derivation of the projection operator on the range of a matrix, using completion of squares. • Solutions of under and over constrained linear equations. Notice that this recitation note is an alternative discussion of the least-squares problem which is more difficult than the one you can find ...

least squares solutions of inconsistent fuzzy linear matrix equations

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An order downdating algorithm for tracking system order and parameters in recursive least squares identification

In this correspondence, a new time and order recursive method for on-line tracking of system order and parameters using recursive least squares (RLS) is presented. The method consists of two parts: a time updating portion that uses existing RLS inverse QR decomposition algorithms and a new computationally efficient “order downdating” portion that calculates the model parameters and residual err...