Related papers: Algorithmic constructions of unitary matrices and …

Nature provides us with a restricted set of microscopic interactions. The question is whether we can synthesize out of these fundamental interactions an arbitrary unitary operator. In this paper we present a constructive algorithm for…

A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…

Fusion frames are a convenient tool in applications where we deal with a large amount of data or when a combination of local data is needed. Oblique dual fusion frames are suitable in situations where the analysis for the data and its…

Machine Learning with deep neural networks has transformed computational approaches to scientific and engineering problems. Central to many of these advancements are precisely tuned neural architectures that are tailored to the domains in…

When modeling microstructures, the computational resource requirements increase rapidly as the simulation domain becomes larger. As a result, simulating a small representative fraction under periodic boundary conditions is often a necessary…

We develop an efficient algorithm for sampling the eigenvalues of random matrices distributed according to the Haar measure over the orthogonal or unitary group. Our technique samples directly a factorization of the Hessenberg form of such…

Consider the collection of all binary matrices having a specific sequence of row and column sums and consider sampling binary matrices uniformly from this collection. Practical algorithms for exact uniform sampling are not known, but there…

In this paper we have considered a finite unitary matrix group with exact elements being unknown and only approximate elements available. Such a group becomes inconsistent with its own multiplication table. We found simple correction…

Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…

Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…

In this study, an algorithm for computing the inverse of periodic k banded matrices, which are needed for solving the differential equations by using the finite differences, the solution of partial differential equations and the solution of…

The exact recovery property of Basis pursuit (BP) and Orthogonal Matching Pursuit (OMP) has a relation with the coherence of the underlying frame. A frame with low coherence provides better guarantees for exact recovery. In particular,…

Equiangular tight frames (ETFs) and biangular tight frames (BTFs) - sets of unit vectors with basis-like properties whose pairwise absolute inner products admit exactly one or two values, respectively - are useful for many applications. A…

Sets of $d\times d$ matrices sharing a common invariant cone enjoy special properties, which are widely used in applications. However, finding this cone or even proving its existence/non-existence is hard. This problem is known to be…

This paper presents an optimization approach for generating custom manipulator configurations using a proposed unconventional modular library. An end-to-end solution is presented in which the resulting optimal models of the modular…

Coupled tensor decompositions (CTDs) perform data fusion by linking factors from different datasets. Although many CTDs have been already proposed, current works do not address important challenges of data fusion, where: 1) the datasets are…

Frames for operators or k-frames were recently considered by Gavruta (2012) in connection with atomic systems. Also generalized frames are important frames in the Hilbert space of bounded linear operators. Fusion frames, which are a special…

In this paper we give a new construction of parametric families of complex Hadamard matrices of square orders, and connect them to equiangular tight frames. The results presented here generalize some of the recent ideas of Bodmann et al.…

We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices. The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated (we consider…

This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality…