323 citations · 346 across the 14 of their papers we have counts for
13 papers · 1 filter
Neural Network Approximation
Ronald DeVore, Boris Hanin, Guergana Petrova
Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. Howev…
Optimal Stable Nonlinear Approximation
Albert Cohen, Ronald DeVore, Guergana Petrova +1
While it is well known that nonlinear methods of approximation can often perform dramatically better than linear methods, there are still questions on how to measure the optimal pe…
Nonlinear Methods for Model Reduction
Andrea Bonito, Albert Cohen, Ronald DeVore +3
The usual approach to model reduction for parametric partial differential equations (PDEs) is to construct a linear space which approximates well the solution manifold $\math…
Polynomial Approximation of Anisotropic Analytic Functions of Several Variables
Andrea Bonito, Ronald DeVore, Diane Guignard +2
Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomia…
Optimal reduced model algorithms for data-based state estimation
Albert Cohen, Wolfgang Dahmen, Ron DeVore +3
Reduced model spaces, such as reduced basis and polynomial chaos, are linear spaces of finite dimension which are designed for the efficient approximation of families par…
Reduced Basis Greedy Selection Using Random Training Sets
Albert Cohen, Wolfgang Dahmen, Ronald DeVore
Reduced bases have been introduced for the approximation of parametrized PDEs in applications where many online queries are required. Their numerical efficiency for such problems h…