Abstract: We consider iterative gradient-based optimization algorithms applied to functions that are smooth and strongly convex. The fastest globally convergent algorithm for this class of functions ...

Abstract: Real-world analog systems, such as photonic neural networks, intrinsically suffer from noise that can impede model convergence and accuracy for a variety of deep learning models. In the ...

Harmonic functions, defined as twice continuously differentiable functions satisfying Laplace’s equation, have long been a subject of intense study in both pure and applied mathematics. Their ...

Let X be a normed linear space, Un an n-dimensional Chebyshev subspace of X. For f ∈ X denote by p(f) ∈ Un its best approximation in Un. The problem of strong unicity consists in estimating how fast ...

We consider shape-restricted nonparametric regression on a closed set X ⊂ ℝ, where it is reasonable to assume that the function has no more than H local extrema interior to X. Following a Bayesian ...