相关论文: Formal power series

Linear exact modeling is a problem coming from system identification: Given a set of observed trajectories, the goal is find a model (usually, a system of partial differential and/or difference equations) that explains the data as precisely…

This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…

To obtain the highest confidence on the correction of numerical simulation programs for the resolution of Partial Differential Equations (PDEs), one has to formalize the mathematical notions and results that allow to establish the soundness…

This paper derives a way to express differentiable complex-valued functions as the sum of powers of $(1-e^{\lambda x})$, where $\lambda\in\mathbb{R}$, with an explicit formula for the remainder. This formulation is then used to associate an…

The Topological Signal Processing (TSP) framework has been recently developed to analyze signals defined over simplicial complexes, i.e. topological spaces represented by finite sets of elements that are closed under inclusion of subsets…

We advance a general theory of coherent preference that surrenders restrictions embodied in orthodox doctrine. This theory enjoys the property that any preference system admits extension to a complete system of preferences, provided it…

This thesis develops signal-processing algorithms and implementation schemes under constraints of minimal parallelism and memory space, with the goal of improving energy efficiency of low-power computing hardware. We propose (i) a…

We consider the approximation of the inverse of the finite element stiffness matrix in the data sparse $\mathcal{H}$-matrix format. For a large class of shape regular but possibly non-uniform meshes including graded meshes, we prove that…

In this paper, a novel linear formulation for power system state estimation that simultaneously treats conventional and synchrophasor measurements is proposed. A linear circuit model for conventional measurements is introduced to enable a…

This article is devoted to the study of a general class of Hamiltonian systems which extends the Calogero systems with external quadratic potential associated to any root system. The interest for such a class comes from a previous article…

A term $a_n$ is $m$-fold hypergeometric, for a given positive integer $m$, if the ratio $a_{n+m}/a_n$ is a rational function over a field $K$ of characteristic zero. We establish the structure of holonomic recurrence equation, i.e. linear…

We present a super-high-efficiency approximate computing scheme for series sum and discrete Fourier transform. The summation of a series sum or a discrete Fourier transform is approximated by summing over part of the terms multiplied by…

In this paper, we propose a numerical method for computing Hadamard finite-part integrals with an integral-power singularity at an endpoint, the part of the divergent integral which is finite as a limiting procedure. In the proposed method,…

The Kohn-Sham method uses a single model system, and corrects it by a density functional the exact user friendly expression of which is not known and is replaced by an approximated, usable, model. We propose to use instead more than one…

We introduce a functional matrix product state (FMPS) based method for simulating the real-space representation of continuous-variable (CV) quantum computation. This approach efficiently simulates non-Gaussian CV systems by leveraging their…

We extend the work of A. Ciaffaglione and P. Di Gianantonio on mechanical verification of algorithms for exact computation on real numbers, using infinite streams of digits implemented as co-inductive types. Four aspects are studied: the…

This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent…

Given the importance of floating-point~(FP) performance in numerous domains, several new variants of FP and its alternatives have been proposed (e.g., Bfloat16, TensorFloat32, and Posits). These representations do not have correctly rounded…

It is described how the Hermite-Pad\'e polynomials corresponding to an algebraic approximant for a power series may be used to predict coefficients of the power series that have not been used to compute the Hermite-Pad\'e polynomials. A…

The characteristic functions of multivariate Feller processes with generator of affine type, and with smooth symbol functions have an explicit representation in terms of power series with rational number coefficients and with monmoms…