Let ? be an open connected subset of the complex plane C and let T be a bounded linear operator on a Hilbert space H. For ? in ? let e the orthogonal projection onto the null-space of T-?I . We discuss the necessary and sufficient conditions for the map ?? to b e continuous on ?. A generalized Gram- Schmidt process is also given.

c © 2006 by John von Neumann Institute for Computing Permission to make digital or hard copies of portions of this work for personal or classroom use is granted provided that the copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise requires prior specific permission by the publisher ment...

Model reduction techniques are needed to directly solve the chemical master equation (CME) due to its enormous size. We recently described an algorithm that solved the CME by combining the finite state projection, stochastic simulation algorithm and Krylov subspace approximations. In this work, we add further improvements that consist of an incomplete orthogonalization process with Krylov subsp...

The nonlinear integral equation P (x) = ∫ β α dy w(y)P (y)P (x + y) is investigated. It is shown that for a given function w(x) the equation admits an infinite set of polynomial solutions P (x). For polynomial solutions, this nonlinear integral equation reduces to a finite set of coupled linear algebraic equations for the coefficients of the polynomials. Interestingly, the set of polynomial sol...

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...

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.