Related papers: Deriving Algorithms for Triangular Tridiagonalizat…
The factorization of skew-symmetric matrices is a critically understudied area of dense linear algebra, particularly in comparison to that of general and symmetric matrices. While some algorithms can be adapted from the symmetric case, the…
The FLAME methodology for deriving linear algebra algorithms from specification, first introduced around 2000, has been successfully applied to a broad cross section of operations. An open question has been whether it can yield algorithms…
The FLAME methodology makes it possible to derive provably correct algorithms from a formal description of a linear algebra problem. So far, the methodology has been successfully used to automate the derivation of direct algorithms such as…
We present a novel recursive algorithm for reducing a symmetric matrix to a triangular factorization which reveals the rank profile matrix. That is, the algorithm computes a factorization $\mathbf{P}^T\mathbf{A}\mathbf{P} =…
In this paper we develop algorithms for orthogonal similarity transformations of skew-symmetric matrices to simpler forms. The first algorithm is similar to the algorithm for the block antitriangular factorization of symmetric matrices, but…
Cut-based directed graph (digraph) clustering often focuses on finding dense within-cluster or sparse between-cluster connections, similar to cut-based undirected graph clustering methods. In contrast, for flow-based clusterings the edges…
Deterministic recursive algorithms for the computation of matrix triangular decompositions with permutations like LU and Bruhat decomposition are presented for the case of commutative domains. This decomposition can be considered as a…
We introduce the ``skew apolarity lemma'' and we use it to give algorithms for the skew-symmetric rank and the decompositions of tensors in {$\bigwedge^dV_{\mathbb{C}}$ with $d\leq 3$ and $\dim V_{\mathbb{C}} \leq 8$}. New algorithms to…
In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new…
The proposed numerical method, "FLAME-slab," solves electromagnetic wave scattering problems for aperiodic slab structures by exploiting short-range regularities in these structures. The computational procedure involves special difference…
Some skew-symmetrizable integer exchange matrices are associated to ideal (tagged) triangulations of marked bordered surfaces. These exchange matrices admits unfoldings to skew-symmetric matrices. We develop an combinatorial algorithm that…
The decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations…
In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems,…
We introduce FLAME, a machine-learning algorithm designed to fit Voigt profiles to HI Lyman-alpha (Ly$\alpha$) absorption lines using deep convolutional neural networks. FLAME integrates two algorithms: the first determines the number of…
Computing the Pfaffian of a skew-symmetric matrix is a problem that arises in various fields of physics. Both computing the Pfaffian and a related problem, computing the canonical form of a skew-symmetric matrix under unitary congruence,…
We propose a new method for computing the eigenvalue decomposition of a dense real normal matrix $A$ through the decomposition of its skew-symmetric part. The method relies on algorithms that are known to be efficiently implemented, such as…
The recently developed Flexible Local Approximation MEthod (FLAME) produces accurate difference schemes by replacing the usual Taylor expansion with Trefftz functions -- local solutions of the underlying differential equation. This paper…
We consider the formal reduction of a system of linear differential equations and show that, if the system can be block-diagonalised through transformation with a ramified Shearing-transformation and following application of the Splitting…
FLAME is a software package to perform a wide range of atomistic simulations for exploring the potential energy surfaces (PES) of complex condensed matter systems. The range of methods include molecular dynamics simulations to sample free…
In recent work, robust mixture modelling approaches using skewed distributions have been explored to accommodate asymmetric data. We introduce parsimony by developing skew-t and skew-normal analogues of the popular GPCM family that employ…