We consider the Modified Gram-Schmidt orthogonalization applied to a matrix A ∈ Rm×n. This corresponds to a QR factorization : A = QR. We study this algorithm in finite precision computation when the matrix A has a numerical rank deficiency k. This subject has already been dealt with success by Björck and Paige in 1992 [1]. They give useful bounds in term of norms. We extend their results to pr...

The standard ratio of spatial resolution between bands for high resolution satellites is 1:4, which is typical when combining images obtained from the same sensor. However, the cost of simultaneously purchasing a set of panchromatic and multispectral images is still relatively high. There is therefore a need to develop methods of data fusion of very high resolution panchromatic imagery with low...

Active metric learning is the problem of incrementally selecting high-utility batches training data (typically, ordered triplets) to annotate, in order progressively improve a learned model over some input domain as rapidly possible. Standard approaches, which independently assess informativeness each triplet batch, are susceptible highly correlated with many redundant triplets and hence low ov...

A new Density-Functional (DF) formula is constructed for atoms. The kinetic energy of the electrons is divided into two parts: the kinetic self-energy and the orthogonalization energy where these concepts are borrowed from the pseudopotential theory. For the radial part of the orthogonalization energy which replaces the radial part of the Fermi-energy of the Thomas-Fermi model we derived the ex...

About SLEPc Technical Reports: These reports are part of the documentation of slepc, the Scalable Library for Eigenvalue Problem Computations. They are intended to complement the Users Guide by providing technical details that normal users typically do not need to know but may be of interest for more advanced users.

In this paper we give first results for the approximation of eb, i.e. the matrix exponential times a vector, using the incomplete orthogonalization method. The benefits compared to the Arnoldi iteration are clear: shorter orthogonalization lengths make the algorithm faster and a large memory saving is also possible. For the case of three term orthogonalization recursions, simple error bounds ar...

In a study of articles published in the Proceedings of the National Academy of Sciences, Gunther Eysenbach discovered a significant citation advantage for those articles made freely-available upon publication (Eysenbach 2006). While the author attempted to control for confounding factors that may have explained the citation differential, the study was unable to control for characteristics of th...