Related papers: Generalized Bruhat decomposition in commutative do…
We consider the problem of recovering a unitary eigendecomposition of a complex unitary matrix from that of its embedded real-valued formulation. Such formulations arise naturally in scientific computing workflows that employ…
We give a simple presentation of the combinatorics of renormalization in perturbative quantum field theory in terms of triangular matrices. The prescription, that may be of calculational value, is derived from first principles, to wit, the…
The polar decomposition for a matrix $A$ is $A=UB$, where $B$ is a positive Hermitian matrix and $U$ is unitary (or, if $A$ is not square, an isometry). This paper shows that the ability to apply a Hamiltonian $\pmatrix{ 0 & A^\dagger \cr A…
The joint problem of reconstruction / feature extraction is a challenging task in image processing. It consists in performing, in a joint manner, the restoration of an image and the extraction of its features. In this work, we firstly…
This paper presents a parametrization of a degenerate density matrix. The problem needs to be approached first with a diagonalized form (the spectral representation) to deal with degeneracy. Such a form is useful for this parametrization in…
The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups. Such a decomposition is needed in order to apply the Abelian hidden subgroup algorithm. Such a decomposition (assuming the Generalized Riemann…
Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…
We develop a generalized hybrid iterative approach for computing solutions to large-scale Bayesian inverse problems. We consider a hybrid algorithm based on the generalized Golub-Kahan bidiagonalization for computing Tikhonov regularized…
We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary…
A Moutard type transformation for matrix generalized analytic functions is derived. Relations between Moutard type transforms and gauge transformations are demonstrated.
We explore new approaches for finding matrix multiplication algorithms in the commutative setting by adapting the flip graph technique: a method previously shown to be effective for discovering fast algorithms in the non-commutative case.…
This Paper conducts a thorough simulation study to assess the effectiveness of various acceleration techniques designed to enhance the conjugate gradient algorithm, which is used for solving large linear systems to accelerate Bayesian…
Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix…
Primary decomposition is a very important tool of commutative algebra and geometry. In this paper we generalized some of the existing algorithms of primary decomposition developed by Eisenbud et al. (cf. [EHV]) for free modules and also…
A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…
We present a new technique to obtain polynomial decay estimates for the matrix coefficients of unitary operators. Our approach, based on commutator methods, applies to nets of unitary operators, unitary representations of topological…
We describe a general approach for computing generators for elimination ideals associated with matrix and hypermatrix spectral decomposition constraints. We derive from these generators iterative procedures for approximating the spectral…
We shall derive and propose several efficient overlapping domain decomposition methods for solving some typical linear inverse problems, including the identiffication of the flux, the source strength and the initial temperature in second…