Convergence of Constrained Anderson Acceleration

We prove non asymptotic linear convergence rates for the constrained Anderson acceleration extrapolation scheme. These guarantees come from new upper bounds on the constrained Chebyshev problem, which consists in minimizing the maximum absolute value of a polynomial on a bounded real interval with $l_1$ constraints on its coefficients vector. Constrained Anderson Acceleration has a numerical cost comparable to that of the original scheme.