BSSE algorithms  Each keyword is considered as a vector in order to perform inner product during the search phase.  Boolean symmetric searchable encryption BSSE is mainly based on the orthogonalization of the keyword field according to the GramSchmidt process.  Searchable encryption: Searching encrypted keywords using encrypted queries (trapdoor) in order to retrieve encrypted documents with...

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.

We discuss some features of the orthogonalization methods commonly applied to QSPR QSAR studies. We outline the well known multivariable linear regression analysis in vector form in order to compare mainly Randic and Gram-Schmidt orthogonalization procedures and also cast the basis for other approaches like Löwdin’s one. We expect that present review may become the starting point for future dev...

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...

The most eeective and widely used methods for integrating the Orr-Sommerfeld equation by shooting are the continuous orthogonalization method and the compound matrix method. In this paper, we consider this problem from a diierential-geometric point of view. A new deenition of orthogonalization is presented: restriction of the Orr-Sommerfeld to a complex Stiefel manifold, and this deenition lead...

It is well-known that orthogonalization of column vectors in a rectangular matrix B with respect to the bilinear form induced by a nonsingular symmetric indefinite matrix A can be seen as its factorization B = QR that is equivalent to the Cholesky-like factorization in the form BTAB = RTΩR, where Ω is some signature matrix. Under the assumption of nonzero principal minors of the matrix M = BTAB...