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Solving dual quaternion equations is an important issue in many fields such as scientific computing and engineering applications. In this paper, we first introduce a new metric function for dual quaternion matrices. Then, we reformulate…
We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in…
We show that the Bellman operator underlying the options framework leads to a matrix splitting, an approach traditionally used to speed up convergence of iterative solvers for large linear systems of equations. Based on standard comparison…
We introduce a duality for Affine Iterated Function Systems (AIFS) which is naturally motivated by group duality in the context of traditional harmonic analysis. Our affine systems yield fractals defined by iteration of contractive affine…
In this work, we consider a rational approximation of the exponential function to design an algorithm for computing matrix exponential in the Hermitian case. Using partial fraction decomposition, we obtain a parallelizable method, where the…
Various approaches to iterative refinement (IR) for least-squares problems have been proposed in the literature and it may not be clear which approach is suitable for a given problem. We consider three approaches to IR for least-squares…
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
An algorithm is discussed for converting a class of recursive processes to a parallel system. It is argued that this algorithm can be superior to certain methods currently found in the literature for an important subset of problems. The…
Given a full column rank matrix $A \in \mathbb{R}^{m\times n}$ ($m\geq n$), we consider a special class of linear systems of the form $A^\top Ax=A^\top b+c$ with $x, c \in \mathbb{R}^{n}$ and $b \in \mathbb{R}^{m}$. The occurrence of $c$ in…
Waveguide and resonant properties of diffractive structures are often explained through the complex poles of their scattering matrices. Numerical methods for calculating poles of the scattering matrix with applications in grating theory are…
We make an experimental comparison of methods for computing the numerical radius of an $n\times n$ complex matrix, based on two well-known characterizations, the first a nonconvex optimization problem in one real variable and the second a…
A few iterations of alternating least squares with a random starting point provably suffice to produce nearly optimal spectral- and Frobenius-norm accuracies of low-rank approximations to a matrix; iterating to convergence is unnecessary.…
In this paper, we study products of asymmetric Toeplitz matrices, we give necessary and sufficient conditions for the product of two asymmetric Toeplitz matrices compatible sizes is asymmetric Toeplitz matrix. We also give some results…
This paper proposes an original problem of \emph{stereo computation from a single mixture image}-- a challenging problem that had not been researched before. The goal is to separate (\ie, unmix) a single mixture image into two constitute…
The scattering matrix, which quantifies the optical reflection and transmission of a photonic structure, is pivotal for understanding the performance of the structure. In many photonic design tasks, it is also desired to know how the…
In this note we establish some appropriate conditions for stochastic equality of two random variables/vectors which are ordered with respect to convex ordering or with respect to supermodular ordering. Multivariate extensions of this result…
This article has been written for an educational magazine whose target audience consists of students and teachers of mathematics in universities, colleges and schools. It concerns a notion of duality between rectangles. A proof is given…
We present applications of rectangular matrix models to various combinatorial problems, among which the enumeration of face-bicolored graphs with prescribed vertex degrees, and vertex-tricolored triangulations. We also mention possible…
A correlation between the symmetry of NMR spectra, including higher-order spectra, and the properties of the spin system has been established. It is shown that for a spectrum to be symmetric about the mid-resonance frequency ({\nu}0), two…
A square matrix of order $n$ with $n\geq 2$ is called a \textit{permutative matrix} or permutative when all its rows (up to the first one) are permutations of precisely its first row. In this paper, the spectra of a class of permutative…