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Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…

Nonlinear least-squares problems are a special class of unconstrained optimization problems in which their gradient and Hessian have special structures. In this paper, we exploit these structures and proposed a matrix-free algorithm with a…

Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the…

In this article we will analyse how to compute the contribution of each input value to its aggregate output in some nonlinear models. Regression and classification applications, together with related algorithms for deep neural networks are…

A subalgebraic approximation algorithm is proposed to estimate from a set of time series the parameters of the observer representation of a discrete-time polynomial system without inputs which can generate an approximation of the observed…

Based the homogeneous balance method, a general method is suggested to obtain several kinds of exact solutions for some kinds of nonlinear equations. The validity and reliability of the method are tested by applying it to the Bousseneq…

Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…

This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…

This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation…

Lattice gas algorithms (LGA) are a class of algorithms including, in chronological order, binary lattice gas cellular automata (LGCA), integer lattice gas algorithms (ILGA) and lattice Boltzmann method (LBM). They are largely used for…

We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to…

This report aims at presenting (yet) a(nother) methodology to design and implement a linear controller for linear dynamical systems on practical applications. The specificity of this report is that authors try to cover (obviously in a non…

As modern architectures introduce additional heterogeneity and parallelism, we look for ways to deal with this that do not involve specialising software to every platform. In this paper, we take the Join Calculus, an elegant model for…

A nonlinear MPC framework is presented that is suitable for dynamical systems with sampling times in the (sub)millisecond range and that allows for an efficient implementation on embedded hardware. The algorithm is based on an augmented…

Heterogeneous computing systems, which combine general-purpose processors with specialized accelerators, are increasingly important for optimizing the performance of modern applications. A central challenge is to decide which parts of an…

A novel algorithm for producing smooth nonlinearities on digital hardware is presented. The non-linearities are inherently quadratic and have both symmetrical and asymmetrical variants. The integer (and fixed point) implementation is highly…

Simulation-based verification algorithms can provide formal safety guarantees for nonlinear and hybrid systems. The previous algorithms rely on user provided model annotations called discrepancy function, which are crucial for computing…

This paper addresses the positive synchronization of interconnected systems on undirected graphs. For homogeneous positive systems, a static feedback protocol design is proposed, based on the Linear Regulator problem. The solution to the…

Approximate computing is a research area where we investigate a wide spectrum of techniques to trade off computation accuracy for better performance or energy consumption. In this work, we provide a general introduction to approximate…

This paper introduces a novel approach to system identification for nonlinear input-output models that minimizes the simulation error and frames the problem as a constrained optimization task. The proposed method addresses vanishing…