Related papers: Algorithms for Simultaneous Block Triangularizatio…
Let $\mathcal{A}=(A_{1},...,A_{n},...)$ be a finite or infinite sequence of $2\times2$ matrices with entries in an integral domain. We show that, except for a very special case, $\mathcal{A}$ is (simultaneously) triangularizable if and only…
In this note, we present an algorithm that yields many new methods for constructing doubly stochastic and symmetric doubly stochastic matrices for the inverse eigenvalue problem. In addition, we introduce new open problems in this area that…
We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…
Two methods to decompose block matrices analogous to Singular Matrix Decomposition are proposed, one yielding the so called economy decomposition, and other yielding the full decomposition. This method is devised to avoid handling matrices…
Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
The task of analytically diagonalizing a tridiagonal matrix can be considerably simplified when a part of the matrix is uniform. Such quasi-uniform matrices occur in several physical contexts, both classical and quantum, where…
We present a scalable approach for simplifying the stability analysis of cluster synchronization patterns on directed networks. When a network has directional couplings, decomposition of the coupling matrix into independent blocks (which in…
In this work, we present an algorithm for the diagonalization of the Integration-by-Parts (IBP) equations. Diagonalized IBP equations are indispensable for reducing loop integrals with high numerator powers to master integrals and for…
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…
We study preconditioned gradient-based optimization methods where the preconditioning matrix has block-diagonal form. Such a structural constraint comes with the advantage that the update computation is block-separable and can be…
The enumeration of finite models is very important to the working discrete mathematician (algebra, graph theory, etc) and hence the search for effective methods to do this task is a critical goal in discrete computational mathematics.…
Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected dimensions of the tensor. It is generalization of approximate…
We study certain linear algebra algorithms for recursive block matrices. This representation has useful practical and theoretical properties. We summarize some previous results for block matrix inversion and present some results on…
In this short note we deal with a constructive scheme to decompose a continuous family of matrices $A(\rho)$ asymptotically as $\rho\to0$ into blocks corresponding to groups of eigenvalues of the limit matrix A(0). We also discuss the…
For general complex or real 1-parameter matrix flows $A(t)_{n,n}$ and for time-invariant static matrices $A \in \CC_{n,n}$ alike, this paper considers ways to decompose matrix flows and single matrices globally via one constant matrix…
Finding the inverse of a matrix is an open problem especially when it comes to engineering problems due to their complexity and running time (cost) of matrix inversion algorithms. An optimum strategy to invert a matrix is, first, to reduce…
Various numerical linear algebra problems can be formulated as evaluating bivariate function of matrices. The most notable examples are the Fr\'echet derivative along a direction, the evaluation of (univariate) functions of…
We present a matrix version of a known method of constructing common eigenvectors of two diagonalizable commuting matrices, thus enabling their simultaneous diagonalization. The matrices may have simple eigenvalues of multiplicity greater…
Block encoding is a successful technique used in several powerful quantum algorithms. In this work we provide an explicit quantum circuit for block encoding a sparse matrix with a periodic diagonal structure. The proposed methodology is…