English
Related papers

Related papers: Algorithmic constructions of unitary matrices and …

200 papers

We introduce a general technique to construct tight fusion frames with prescribed symmetries. Applying this technique with a prescription for "all the symmetries", we construct a new family of equi-isoclinic tight fusion frames (EITFFs),…

Combinatorics · Mathematics 2026-01-23 Matthew Fickus , Joseph W. Iverson , John Jasper , Dustin G. Mixon

The increasing size of neural networks has led to a growing demand for methods of efficient fine-tuning. Recently, an orthogonal fine-tuning paradigm was introduced that uses orthogonal matrices for adapting the weights of a pretrained…

Machine Learning · Computer Science 2024-06-17 Mikhail Gorbunov , Nikolay Yudin , Vera Soboleva , Aibek Alanov , Alexey Naumov , Maxim Rakhuba

We survey recent progress on efficient algorithms for approximately diagonalizing a square complex matrix in the models of rational (variable precision) and finite (floating point) arithmetic. This question has been studied across several…

Symbolic Computation · Computer Science 2023-05-19 Nikhil Srivastava

In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the…

Numerical Analysis · Mathematics 2017-08-07 Paola Boito , Yuli Eidelman , Luca Gemignani

In this paper, we study conditions under which a finite subset $Z$ of the unit sphere $S^{d-1}\subset \mathbb{R}^{d}$ becomes a spherical $t$-design, when $Z$ is constructed by the following procedure: starting from a finite set of…

Combinatorics · Mathematics 2026-01-27 Ryutaro Misawa

We propose a general algorithmic framework for constrained matrix and tensor factorization, which is widely used in signal processing and machine learning. The new framework is a hybrid between alternating optimization (AO) and the…

Machine Learning · Statistics 2016-08-24 Kejun Huang , Nicholas D. Sidiropoulos , Athanasios P. Liavas

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

Signal Processing · Electrical Eng. & Systems 2023-07-19 Xiao Fu , Nico Vervliet , Lieven De Lathauwer , Kejun Huang , Nicolas Gillis

The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…

Numerical Analysis · Computer Science 2013-08-28 Rafi Witten , Emmanuel Candes

When constructing finite frames for a given application, the most important consideration is the spectrum of the frame operator. Indeed, the minimum and maximum eigenvalues of the frame operator are the optimal frame bounds, and the frame…

Functional Analysis · Mathematics 2011-06-07 Jameson Cahill , Matthew Fickus , Dustin G. Mixon , Miriam J. Poteet , Nathaniel K. Strawn

Tensor factorization with hard and/or soft constraints has played an important role in signal processing and data analysis. However, existing algorithms for constrained tensor factorization have two drawbacks: (i) they require…

Numerical Analysis · Mathematics 2024-07-01 Shunsuke Ono , Takuma Kasai

Quantum compiling, a process that decomposes the quantum algorithm into a series of hardware-compatible commands or elementary gates, is of fundamental importance for quantum computing. We introduce an efficient algorithm based on deep…

Quantum Physics · Physics 2020-10-22 Yuan-Hang Zhang , Pei-Lin Zheng , Yi Zhang , Dong-Ling Deng

In this paper we address the problem of building a class of robust factorization algorithms that solve for the shape and motion parameters with both affine (weak perspective) and perspective camera models. We introduce a Gaussian/uniform…

Computer Vision and Pattern Recognition · Computer Science 2020-12-16 Andrei Zaharescu , Radu Horaud

In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…

Numerical Analysis · Mathematics 2022-08-11 Andrew V. Terekhov

Several problems in magnetically confined fusion, such as the computation of exterior vacuum fields or the decomposition of the total magnetic field into separate contributions from the plasma and the external sources, are best formulated…

Numerical Analysis · Mathematics 2019-11-25 Dhairya Malhotra , Antoine J. Cerfon , Michael O'Neil , Evan Toler

Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus…

Statistical Mechanics · Physics 2016-08-31 N. Destainville , R. Mosseri , F. bailly

Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in folding applications. We propose a new systematic and broadly…

Computational Geometry · Computer Science 2016-01-22 Jason S. Ku , Erik D. Demaine

Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes with an associated frame operator encoding essential properties of the frame. We…

Combinatorics · Mathematics 2017-11-30 Tim Haga , Christoph Pegel

Branes and defects in topological Landau-Ginzburg models are described by matrix factorisations. We revisit the problem of deforming them and discuss various deformation methods as well as their relations. We have implemented these…

High Energy Physics - Theory · Physics 2012-06-28 Nils Carqueville , Laura Dowdy , Andreas Recknagel

We propose an efficient algorithm for computing a common eigenvector of a finite set of square matrices. As an immediate consequence we obtain an algorithm for determining whether the matrices admit a simultaneous triangulation, and, if so,…

Rings and Algebras · Mathematics 2023-09-27 Emanuel Malvetti

Dimer models (also known as brane tilings) are special bipartite graphs on a torus $\mathbb{T}^2$. They encode the structure of the 4d $\mathcal{N} = 1$ worldvolume theories of D3 branes probing toric affine Calabi-Yau singularities.…

High Energy Physics - Theory · Physics 2021-12-03 Valdo Tatitscheff