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A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…
A numerical scheme for solving the time-evolution of wave functions under the time dependent Kohn-Sham equation has been developed. Since the effective Hamiltonian depends on the wave functions, the wave functions and the effective…
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…
In this paper we extend the polynomial time integration framework to include exponential integration for both partitioned and unpartitioned initial value problems. We then demonstrate the utility of the exponential polynomial framework by…
Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an…
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
We calculate the solution of the Bagley-Torvik equation for arbitrary initial conditions and arbitrary external force as the sum of two terms. The first one is a linear combination of exponentials with error functions, and the second one is…
Based on the generation function of Laguerre polynomials, We proposed a new Laguerre polynomial expansion scheme in the calculation of evolution of time dependent Schr\"odinger equation. Theoretical analysis and numerical test show that the…
We consider convolution integral equations on a finite interval with a real-valued kernel of even parity, a problem equivalent to finding a Wiener-Hopf factorisation of a notoriously difficult class of $2\times 2$ matrices. The kernel…
Ordinary differential equations (ODE's) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the evolution of complex systems and it might consist of high-dimensional…
In this paper, we first present an explicit expression for the inverse\emph{} of a type of matrices. As special applications, the inverse of some matrices arising from implicit time integration techniques, such as the well-known implicit…
Time series analysis is used to understand and predict dynamic processes, including evolving demands in business, weather, markets, and biological rhythms. Exponential smoothing is used in all these domains to obtain simple interpretable…
We present a method for the explicit diagonalization of some Hankel operators. This method allows us to recover classical results on the diagonalization of Hankel operators with the absolutely continuous spectrum. It leads also to new…
Contraction analysis establishes exponential incremental convergence of a nonlinear system by solving a linear matrix inequality for a contraction metric, and has become a standard resource for solving problems in nonlinear control and…
An efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials in the eigenvalue to which the eigenvector is associated, as…
Many real life problems can be reduced to the solution of a complex exponentials approximation problem which is usually ill posed. Recently a new transform for solving this problem, formulated as a specific moments problem in the plane, has…
Using projection between Euclidian spaces of different dimensions, the signal compression and decompression become straightforward. This encoding/decoding technique requires no preassigned measuring matrix as in compressed sensing.…
This paper introduces quantum circuit methodologies for pointwise multiplication and convolution of complex functions, conceptualized as "processing through encoding". Leveraging known techniques, we describe an approach where multiple…
A numerical method is proposed for computing time-periodic and relative time-periodic solutions in dissipative wave systems. In such solutions, the temporal period, and possibly other additional internal parameters such as the propagation…