A general framework for structural preserving model reductions by Krylov subspace projection methods is developed. The goal is to preserve any substructures of importance in the matrices L,G,C,B that define the model prescribed by transfer function H(s) = L∗(G+ sC)−1B. As an application, quadratic transfer functions targeted by Su and Craig (J. Guidance, Control, and Dynamics, 14 (1991), pp. 26...

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.

The statistics of meanders is studied in connection with the Temperley-Lieb algebra. Each (multi-component) meander corresponds to a pair of reduced elements of the algebra. The assignment of a weight q per connected component of meander translates into a bilinear form on the algebra, with a Gram matrix encoding the fine structure of meander numbers. Here, we calculate the associated Gram deter...

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...

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...

This paper is concerned with a technique for solving Fredholm integro-dierentialequations in the reproducing kernel Hilbert space. In contrast with the conventionalreproducing kernel method, the Gram-Schmidt process is omitted hereand satisfactory results are obtained. The analytical solution is represented inthe form of series. An iterative method is given to obtain the approximate solution.Th...

A new criterion for selective reorthogonalization in the Gram-Schmidt procedure is given. We establish its comportment in presence of rounding errors when the criterion is used with modified Gram-Schmidt algorithm and show counter-example matrices which prove that standard criteria are not always valid. Experimentally, our criterion is fine also for the classical Gram-Schmidt algorithm with reo...

A Gram-Schmidt type algorithm is given for finite d-dimensional reflexive forms over division rings. The algorithm uses d/3 + O(d) ring operations. Next, that algorithm is adapted in two new directions. First a sequential algorithm is given whose complexity matches the complexity of matrix multiplication. Second, a parallel NC algorithm is given with similar complexity.

Summary In this article, we formalize the Gram-Schmidt process in Mizar system [2], [3] (compare another formalization using Isabelle/HOL proof assistant [1]). This is one of most famous methods for orthonormalizing a set vectors. The method named after Jørgen Pedersen Gram and Erhard Schmidt [4]. There are many applications field computer science, e.g., error correcting codes or cryptology [8]...