The hybrid precoding problem in point-to-point millimeter wave (mmWave) multiple input output (MIMO) for narrowband channel is established as a Frobenius norm minimization problem. It translated into trace problem, and two algorithms are proposed to solve it. In the first method based on alternating minimization, we alternately determine analog precoder digital precoder, keeping other constant ...

BACKGROUND Left ventricular size and shape are important for quantifying cardiac remodeling in response to cardiovascular disease. Geometric remodeling indices have been shown to have prognostic value in predicting adverse events in the clinical literature, but these often describe interrelated shape changes. We developed a novel method for deriving orthogonal remodeling components directly fro...

The Gram-Schmidt Process (GSP) is used to convert a non-orthogonal basis (a set of linearly independent vectors) into an orthonormal basis (a set of orthogonal, unit-length vectors). The process consists of taking each vector and then subtracting the elements in common with the previous vectors. This paper introduces an Enhanced version of the Gram-Schmidt Process (EGSP) with inverse, which is ...

Maritime surveillance of the Exclusive Economic Zone (EEZ) is a present military and civilian challenge. The High Frequency Surface Wave Radar, as its coverage range is not limited by the radio horizon, is well-suited to fulfil this task. HFSWRs are based on the ability of HF waves (3 MHz to 30 MHz) to propagate along the earth curvature: it is possible to detect targets up to few hundred kilom...

We characterize the class of probability measures for which the multiplicative renormalization method can be applied for the function h(x) = 1 √ 1−x to obtain orthogonal polynomials. It turns out that this class consists of only uniform probability measures on intervals and probability measures being supported by one or two points. 1. Multiplicative Renormalization Method Let μ be a probability...

Let there be given a probability measure μ on the unit circle T of the complex plane and consider the inner product induced by μ. In this paper we consider the problem of orthogonalizing a sequence of monomials {zk}k, for a certain order of the rk ∈ Z, by means of the Gram-Schmidt orthogonalization process. This leads to a basis of orthonormal Laurent polynomials {ψk}k. We show that the matrix ...

Constrained orthogonal polynomials have been recently introduced in the study of the HohenbergKohn functional to provide basis functions satisfying particle number conservation for an expansion of the particle density. More generally, we define block orthogonal (BO) polynomials which are orthogonal, with respect to a first Euclidean inner product, to a given i-dimensional subspace Ei of polynom...

Abstract With the recent realization of exascale performance by Oak Ridge National Laboratory’s Frontier supercomputer, reducing communication in kernels like QR factorization has become even more imperative. Low-synchronization Gram-Schmidt methods, first introduced Świrydowicz et al. ( Numer. Lin. Alg. Appl. 28(2):e2343, 2020), have been shown to improve scalability Arnoldi method high-perfor...