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We present the generating function approach to the perturbative exponentiation of correlators of a product of Wilson lines and loops. The exponentiated expression is presented in closed form as an algebraic function of correlators of known…
Topological entropy serves as a viable candidate for quantifying mixing and complexity of a highly chaotic system. Particularly in turbulence, this is determined as the exponential stretching rate of a fluid material line that typically…
In this paper, we present four constructions of {general} self-orthogonal matrix-product codes associated with Toeplitz matrices. The first one relies on the {dual} of a known {general} dual-containing matrix-product code; the second one is…
In quasi-Monte Carlo methods, generating high-dimensional low discrepancy sequences by generator matrices is a popular and efficient approach. Historically, constructing or finding such generator matrices has been a hard problem. In…
How to calculate the exponential of matrices in an explicit manner is one of fundamental problems in almost all subjects in Science. Especially in Mathematical Physics or Quantum Optics many problems are reduced to this calculation by…
A quasi-Toeplitz $M$-matrix $A$ is an infinite $M$-matrix that can be written as the sum of a semi-infinite Toeplitz matrix and a correction matrix. This paper is concerned with computing the square root of invertible quasi-Toeplitz…
The sensitivity of eigenvalues of structured matrices under general or structured perturbations of the matrix entries has been thoroughly studied in the literature. Error bounds are available and the pseudospectrum can be computed to gain…
A simple and efficient algorithm to numerically compute the genus of surfaces of three-dimensional objects using the Euler characteristic formula is presented. The algorithm applies to objects obtained by thresholding a scalar field in a…
We analyse the convergence of the ergodic formula for Toeplitz matrix-sequences generated by a symbol and we produce explicit bounds depending on the size of the matrix, the regularity of the symbol and the regularity of the test function.
This paper examines the coefficient problems for the class of semigroup generators, a topic in complex dynamics that has recently been studied in context of geometric function theory. Further, sharp bounds of coefficient functional such as…
In this paper we derive new uniform convergence estimates for the V-cycle MGM applied to symmetric positive definite Toeplitz block tridiagonal matrices, by also discussing few connections with previous results. More concretely, the…
We show that the maximum rank of block lower triangular Toeplitz block matrices equals their term rank if the blocks fulfill a structural condition, i.e., only the locations but not the values of their nonzeros are fixed.
The nearest circulant approximation of a real Toeplitz matrix in the Frobenius norm is derived. This matrix is symmetric. It is proven that symmetric circulant matrices are the only real circulant matrices with all real eigenvalues. The…
Using the renewal approach we prove exponential inequalities for additive functionals and empirical processes of ergodic Markov chains, thus obtaining counterparts of inequalities for sums of independent random variables. The inequalities…
We obtain a formula for the determinant of a block Toeplitz matrix associated with a quadratic fermionic chain with complex coupling. Such couplings break reflection symmetry and/or charge conjugation symmetry. We then apply this formula to…
For solving the Poisson equation it is usually possible to discretize it into solving the corresponding linear system $Ax=b$.Variational quantum algorithms (VQAs) for the discreted Poisson equation have been studied before. We give a VQA…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…
In this work we study the convergence properties of the one-level parallel Schwarz method with Robin transmission conditions applied to the one-dimensional and two-dimensional Helmholtz and Maxwell's equations. One-level methods are not…
We present a new algorithm for fast matrix multiplication using tensor decompositions which have special features. Thanks to these features we obtain exponents lower than what the rank of the tensor decomposition suggests. In particular for…
In this paper we use Euler-Seidel matrices method to find out some properties of exponential and geometric polynomials and numbers. Some known results are reproved and some new results are obtained.