Related papers: Efficient computation of matrix elements of generi…
In contrast to the determinant, no algorithm is known for the exact determination of the permanent of a square matrix that runs in time polynomial in its dimension. Consequently, non interacting fermions are classically efficiently…
We calculate the non-forward quark matrix elements of operators with two covariant derivatives needed for the renormalisation of the second moment of generalised parton distributions in one-loop lattice perturbation theory using Wilson…
There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular powerful techniques. Here, we present a…
Two known computation methods and one new computation method for matrix determinant over an integral domain are discussed. For each of the methods we evaluate the computation times for different rings and show that the new method is the…
We present a method for the numerical calculation of derivatives of functions of general complex matrices. The method can be used in combination with any algorithm that evaluates or approximates the desired matrix function, in particular…
SSOR preconditioning of fermion matrix inversions which is parallelized using a locally-lexicographic lattice sub-division, has been shown to be very efficient for standard Wilson fermions. We demonstrate here the power of this method for…
Fermion sampling is to generate probability distribution of a many-body Slater-determinant wavefunction, which is termed "determinantal point process" in statistical analysis. For its inherently-embedded Pauli exclusion principle, its…
A formula expressing the fermionic determinant (a large order polynomial) as an infinite product of smaller determinants is derived and discussed. These smaller determinants are of a fixed size, independent of the size of the lattice and…
In this paper we present two algorithms for the computation of a diagonal form of a matrix over non-commutative Euclidean domain over a field with the help of Gr\"obner bases. This can be viewed as the pre-processing for the computation of…
We establish Plemelj-Smithies formulas for determinants in different algebras of operators. In particular we define a Poincar\'e type determinant for operators on the torus $\Tn$ and deduce formulas for determinants of periodic…
The fermionic determinant of a lattice Dirac operator that obeys the Ginsparg-Wilson relation factorizes into two factors that are complex conjugate of each other. Each factor is naturally associated with a single chiral fermion and can be…
This paper presents new approaches for finding the determinant and inverse of a matrix. The choice of pivot selection is kept arbitrary and can be made according to the users need. So the ill conditioned matrices can be handled easily. The…
We introduce a novel technique for constructing higher-order variational integrators for Hamiltonian systems of ODEs. In particular, we are concerned with generating globally smooth approximations to solutions of a Hamiltonian system. Our…
The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric…
We give a formula for the determinant of an $n\times n$ matrix with entries from a commutative ring with unit. The formula can be evaluated by a "straight-line program" performing only additions, subtractions and multiplications of ring…
We discuss how to resolve generic skew-symmetric and generic symmetric determinantal singularities. The key ingredients are (skew-) symmetry preserving matrix operations in order to deduce an inductive argument.
I discuss the connection between the Hamiltonian and path integral approaches for fermionic fields. I show how the temporal Wilson projection operators appear naturally in a lattice action. I also carefully treat the insertion of a chemical…
The fermionic Gaussian operator basis provides a representation for treating strongly correlated fermion systems, as well as playing an important role in random matrix theory. We prove that a resolution of unity exists for any even…
Fermionic neural network (FermiNet) is a recently proposed wavefunction Ansatz, which is used in variational Monte Carlo (VMC) methods to solve the many-electron Schr\"{o}dinger equation. FermiNet proposes permutation-equivariant…
We present a unified framework for the construction of localized exponential integrators that bypasses the traditional trade-off between the accuracy of global spectral methods and the efficiency of sparse finite differences. By evaluating…