Related papers: Numerical Differentiation using local Chebyshev-Ap…
A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent…
Optimization on manifolds is a class of methods for optimization of an objective function, subject to constraints which are smooth, in the sense that the set of points which satisfy the constraints admits the structure of a differentiable…
Collision detection appears as a canonical operation in a large range of robotics applications from robot control to simulation, including motion planning and estimation. While the seminal works on the topic date back to the 80s, it is only…
Black-box variational inference tries to approximate a complex target distribution though a gradient-based optimization of the parameters of a simpler distribution. Provable convergence guarantees require structural properties of the…
Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of…
We consider the global minimization of smooth functions based solely on function evaluations. Algorithms that achieve the optimal number of function evaluations for a given precision level typically rely on explicitly constructing an…
We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes,…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
Point discretization of curved surfaces is required in many applications ranging from object rendering to the solution of surface partial differential equations (PDEs). These applications often impose that surfaces are sampled with local…
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…
In derivative-free and blackbox optimization, the objective function is often evaluated through the execution of a computer program seen as a blackbox. It can be noisy, in the sense that its outputs are contaminated by random errors.…
A very simple and efficient local variational iteration method for solving problems of nonlinear science is proposed in this paper. The analytical iteration formula of this method is derived first using a general form of first order…
This paper proposes a data-driven approach for computing elasticity by means of a non-parametric regression approach rather than an optimization approach. The Chebyshev approximation is utilized for tackling the material data-sets…
We analyze decay of Chebyshev coefficients and local Chebyshev approximations for functions of finite regularity on finite intervals, focusing on the framework where the interval length tends to zero while the number of approximation nodes…
For any $k\geq 1$, this paper studies the number of polynomials having $k$ irreducible factors (counted with or without multiplicities) in $\mathbf{F}_q[t]$ among different arithmetic progressions. We obtain asymptotic formulas for the…
In this paper, we study neural networks from the point of view of nonsmooth optimisation, namely, quasidifferential calculus. We restrict ourselves to the case of uniform approximation by a neural network without hidden layers, the…
We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable functions is intractable and suffers from the curse of…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
We use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning. In particular, we study gradient descent, proximal gradient…
We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…