Related papers: Recursive numerical calculus of one-loop tensor in…

Tensor operations play an essential role in various fields of science and engineering, including multiway data analysis. In this study, we establish a few basic properties of the range and null space of a tensor using block circulant…

We develop and analyze iterative methods for computing the principal square root of third-order tensors under the T-product framework. Tensor extensions of the Newton iteration (quadratic convergence) and the Denman--Beavers iteration…

We construct a specific formalism for calculating the one-loop virtual corrections for standard model processes with an arbitrary number of external legs. The procedure explicitly separates the infrared and ultraviolet divergences…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

Building on the open-loop algorithm we introduce a new method for the automated construction of one-loop amplitudes and their reduction to scalar integrals. The key idea is that the factorisation of one-loop integrands in a product of loop…

Higher-order tensors appear in various areas of mechanics as well as physics, medicine or earth sciences. As these tensors are highly complex, most are not well understood. Thus, the analysis and the visualization process form a highly…

A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…

In this paper we suggest a new algorithm for the computation of a best rank one approximation of tensors, called alternating singular value decomposition. This method is based on the computation of maximal singular values and the…

Many computational problems can be formulated in terms of high-dimensional functions. Simple representations of such functions and resulting computations with them typically suffer from the "curse of dimensionality", an exponential cost…

A method is presented in which matrix elements for some processes are calculated recursively. This recursive calculational technique is based on the method of basis spinors.

We show how to extract the coefficients of the 4-, 3-, 2- and 1-point one-loop scalar integrals from the full one-loop amplitude of arbitrary scattering processes. In a similar fashion, also the rational terms can be derived. Basically no…

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

We use computational algorithms recently developed by us to study completely four index divergence free quadratic in Riemann tensor polynomials in GR. Some results are new and some other reproduce and/or correct known ones. The algorithms…

We introduce tensor numerical techniques for solving optimal control problems constrained by elliptic operators in $\mathbb{R}^d$, $d=2,3$, with variable coefficients, which can be represented in a low rank separable form. We construct a…

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…

This paper presents iterative methods for solving tensor equations involving the T-product. The proposed approaches apply tensor computations without matrix construction. For each initial tensor, these algorithms solve related problems in a…

We present a new procedure using on-shell recursion to determine coefficients of integral functions appearing in one-loop scattering amplitudes of gauge theories, including QCD. With this procedure, coefficients of integrals, including…

In this paper, we investigate the sample size requirement for a general class of nuclear norm minimization methods for higher order tensor completion. We introduce a class of tensor norms by allowing for different levels of coherence, which…

Generalized inverses of tensors play increasingly important roles in computational mathematics and numerical analysis. It is appropriate to develop the theory of generalized inverses of tensors within the algebraic structure of a ring. In…

A well-established approach to reasoning about loops during program analysis is to capture the effect of a loop by extracting recurrences from the loop; these express relationships between the values of variables, or program properties such…