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In this paper, we introduce a new column selection strategy, named here “Deviation Maximization”, and apply it to compute rank-revealing QR factorizations as an alternative to the well-known block version of the QR factorization with the column pivoting method, called QP3 and currently implemented in LAPACK’s routine. We show that the resulting algorithm, named QRDM, has similar rank-revealing properties of QP3 and better execution times. We present experimental results on a wide data set of numerically singular matrices, which has become a reference in the recent literature.

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We provide a numerical package for the computation of a d-variate near G-optimal polynomial regression design of degree m on a finite design space X ⊂ R d , by few iterations of a basic multiplicative algorithm followed by Tchakaloff-like compression of the discrete measure keeping the reached G-efficiency, via an accelerated version of the Lawson-Hanson algorithm for Non-Negative Least Squares (NNLS) problems. This package can solve on a personal computer large-scale problems where c a r d ( X ) × dim ( P 2 m d ) is up to 10 8 – 10 9 , being dim ( P 2 m d ) = 2 m + d d = 2 m + d 2 m . Several numerical tests are presented on complex shapes in d = 3 and on hypercubes in d > 3 .

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