In this paper we consider the design of spectrally efficient time-limited pulses for ultra-wideband (UWB) systems using an overlapping pulse position modulation scheme. For this we investigate an orthogonalization method, which was developed in 1950 by Löwdin [1, 2]. Our objective is to obtain a set of N orthogonal (Löwdin) pulses, which remain time-limited and spectrally efficient for UWB syst...

This paper presents a feature selection method based on the popular transformation approach: principal component analysis (PCA). It is popular because it finds the optimal solution to several objective functions (including maximum variance and minimum sum-squared-error), and also because it provides an orthogonal basis solution. However, PCA as a dimensionality reduction algorithm do not explic...

For g < n, let b1, . . . , bn−g be n− g independent vectors in R with a common distribution invariant by rotation. Considering these vectors as a basis for the Euclidean lattice they generate, the aim of this paper is to provide asymptotic results when n → +∞ concerning the property that such a random basis is reduced in the sense of Lenstra, Lenstra & Lovász. The proof passes by the study of t...

In the present paper, we propose the global full orthogonalization method (Gl-FOM) and global generalized minimum residual (Gl-GMRES) method for solving large and sparse general coupled matrix equations

5 Normalization and orthogonalization 15 5.1 Admissible physical solutions . . . . . . . . . . . . . . . . . . 16 5.2 Linear normalization . . . . . . . . . . . . . . . . . . . . . . . 16 5.3 Radial normalization . . . . . . . . . . . . . . . . . . . . . . . 18 5.3.1 One dimensional . . . . . . . . . . . . . . . . . . . . . 18 5.3.2 Two dimensional . . . . . . . . . . . . . . . . . . . . . 20 5...

We propose a novel communication design, termed random orthogonalization , for federated learning (FL) in massive multiple-input and multiple-output (MIMO) wireless system. The key novelty of random orthogonalization comes from the tight coupling FL two unique characteristics MIMO - channel har...

We present an Out-of-Core Filter-Diagonalization method which can be used to solve very large electronic structure problems within the framework of the one-electron pseudopotentialbased methods. The approach is based on the following three steps: First, nonorthogonal states in a desired energy range are generated using the filter-diagonalization method. Next, these states are orthogonalized usi...

We present in detail the recently derived ab initio molecular dynamics (AIMD) formalism [Alonso et al. Phys. Rev. Lett. 2008, 101, 096403], which due to its numerical properties, is ideal for simulating the dynamics of systems containing thousands of atoms. A major drawback of traditional AIMD methods is the necessity to enforce the orthogonalization of the wave functions, which can become the ...

We propose a new uniform framework of Compact Rational Krylov (CORK) methods for solving large-scale nonlinear eigenvalue problems: A(λ)x = 0. For many years, linearizations are used for solving polynomial and rational eigenvalue problems. On the other hand, for the general nonlinear case, A(λ) can first be approximated by a (rational) matrix polynomial and then a convenient linearization is us...