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...

We propose an alternative orthonormalization method that computes the orthonor-mal basis from the right singular vectors of a matrix. Its advantage are: a) all operations are matrix-matrix multiplications and thus cache-eecient, b) only one synchronization point is required in parallel implementations, c) could be more stable than Gram-Schmidt. In addition, we consider the problem of incrementa...

The prediction of the electric (E) field plays an important role in monitoring radiofrequency electromagnetic (RF-EMF) exposure induced by cellular networks. In this paper, we present approach to extrapolate E urban area using artificial neural network. We first apply a moving average method over sliding window out EMF random fluctuations and remove noise produced during drive test recording me...

We discuss the general formation of complementary behaviors, functions and forms in biological species competing for resources. We call orthogonalization the related processes on macro and micro-level of a self-organized formation of correlations in the species properties. Orthogonalization processes could be, for example, easily observed in sympatric speciation, as we show in numerical studies...

In this work, we consider a radar system where the antenna elements are arbitrarily distributed in space with several hundred wavelengths away. We call such a radar system distributed aperture radar system. We assume that the system is operating in multi-pathing environment, such as an urban area. We present methods for designing clutter rejecting waveforms and for reconstruction of reflectivit...

An important geometric and linear algebraic problem denoted as vector orthogonalization, fundamental to handle contact detection and contact force descriptions in engineering applications, is here considered. The problem is to find a set of linearly independent vectors that span the entire R3 Euclidean space given only one of the base vectors. This paper contains the explanation on how theHouse...

The occurrence of collinearity in fMRI-based GLMs (general linear models) may reduce power or produce unreliable parameter estimates. It is commonly believed that orthogonalizing collinear regressors in the model will solve this problem, and some software packages apply automatic orthogonalization. However, the effects of orthogonalization on the interpretation of the resulting parameter estima...

In this article we present a fast recursive orthogonalization scheme for two important subspaces of the Macaulay matrix: its row space and null space. It requires a graded monomial ordering and exploits the resulting structure of the Macaulay matrix induced by this graded ordering. The resulting orthogonal basis for the row space will retain a similar structure as the Macaulay matrix and is as ...

This paper describes modeling discrete event systems in Metropolis using one of the key concepts employed by Metropolis, orthogonalization of design aspects, which in this particular case, is the orthogonalization between capability and cost. To support the orthogonalization, quantity annotation mechanism is introduced. This paper formally analyzes simulation strategies for quantity annotation ...