Related papers: GR decompositions and their relations to Cholesky-…
We obtain several analogs of real polar decomposition for even dimensional matrices. In particular, we decompose a non-degenerate matrix as a product of a Hamiltonian and an anti-symplectic matrix and under additional requirements we…
Ultradiscretization is a limiting procedure transforming a given difference equation into a cellular automaton. In addition the cellular automaton constructed by this procedure preserves the essential properties of the original equation,…
Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help understand condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for…
In this paper we introduce the algorithm and the fixed point hardware to calculate the normalized singular value decomposition of a non-symmetric matrices using Givens fast (approximate) rotations. This algorithm only uses the basic…
Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In…
This work sets the non isotropic noncentral elliptical shape distributions via QR decomposition in the context of zonal polynomials, avoiding the invariant polynomials and the open problems for their computation. The new shape distributions…
New real structure-preserving decompositions are introduced to develop fast and robust algorithms for the (right) eigenproblem of general quaternion matrices. Under the orthogonally JRS-symplectic transformations, the Francis JRS-QR step…
In this paper, we generalize Spencer's hyperbolic cosine algorithm to the matrix-valued setting. We apply the proposed algorithm to several problems by analyzing its computational efficiency under two special cases of matrices; one in which…
Matrix decomposition is a very important mathematical tool in numerical linear algebra for data processing. In this paper, we introduce a new randomized matrix decomposition algorithm, which is called randomized approximate SVD based on…
A parametrization, given by the Euler angles, of Hermitian matrix generators of even and odd-degenerate Clifford algebras is constructed by means of the Kronecker product of a parametrized version of Pauli matrices and by the identification…
Aiming to alleviate data sparsity and cold-start problems of traditional recommender systems, incorporating knowledge graphs (KGs) to supplement auxiliary information has recently gained considerable attention. Via unifying the KG with…
Let $q=2^f$, and let $G=\mathrm{SO}_8^+(q)$ and $U$ be a Sylow $2$-subgroup of $G$. We first describe the fusion of the conjugacy classes of $U$ in $G$. We then use this information to prove the unitriangularity of the $\ell$-decomposition…
The canonical polyadic (CP) decomposition is one of the most widely used tensor decomposition techniques. The conventional CP decomposition algorithm combines alternating least squares (ALS) with the normal equation. However, the normal…
We consider a Canonical Polyadic (CP) decomposition approach to low-rank tensor completion (LRTC) by incorporating external pairwise similarity relations through graph Laplacian regularization on the CP factor matrices. The usage of graph…
In this paper an approach for finding a sparse incomplete Cholesky factor through an incomplete orthogonal factorization with Givens rotations is discussed and applied to Gaussian Markov random fields (GMRFs). The incomplete Cholesky factor…
Classical approaches in cluster analysis are typically based on a feature space analysis. However, many applications lead to datasets with additional spatial information and a ground truth with spatially coherent classes, which will not…
An efficient decoding algorithm named `divided decoder' is proposed in this paper. Divided decoding can be combined with any decoder using QR-decomposition and offers different pairs of performance and complexity. Divided decoding provides…
We make a full landscape analysis of the (generally non-convex) orthogonal Procrustes problem. This problem is equivalent to computing the polar factor of a square matrix. We reveal a convexity-like structure, which explains the already…
Vector set orthogonal normalization and matrix QR decomposition are fundamental problems in matrix analysis with important applications in many fields. We know that Gram-Schmidt process is a widely used method to solve these two problems.…
We present fast numerical methods for computing the Hessenberg reduction of a unitary plus low-rank matrix $A=G+U V^H$, where $G\in \mathbb C^{n\times n}$ is a unitary matrix represented in some compressed format using $O(nk)$ parameters…