A generalization of Sliced Inverse Regression to functional regressors was introduced by Ferré and Yao (2003). Here we first address the issue of the identifiability of the Effective Dimension Reduction (EDR) space. Next, we estimate the covariance operator of the conditional expectation by means of kernel estimates. Consistency is proved and this extends the results of Zhu and Fang (1996) in t...

A class of smoothed point interpolation methods (smoothed PIMs) are introduced in this paper, which are derived from the smoothed Galerkin weak-form for variational formulation based on the gradient smoothing techniques [1]. In the scheme of smoothed PIMs, the strain smoothing operation [2] can be applied on different types of smoothing domains which are constructed centring at field nodes, edg...

We introduce the smoothed analysis of algorithms, which is a hybrid of the worst-case and average-case analysis of algorithms. In smoothed analysis, we measure the maximum over inputs of the expected performance of an algorithm under small random perturbations of that input. We measure this performance in terms of both the input size and the magnitude of the perturbations. We show that the simp...

We introduce the smoothed analysis of algorithms, which is a hybrid of the worst-case and average-case analysis of algorithms. In smoothed analysis, we measure the maximum over inputs of the expected performance of an algorithm under small random perturbations of that input. We measure this performance in terms of both the input size and the magnitude of the perturbations. We show that the simp...

We propose a method of outer approximations, with each approximate problem smoothed using entropic regularization, to solve continuous min-max problems. By using a well-known uniform error estimate for entropic regularization, convergence of the overall method is shown while allowing each smoothed problem to be solved inexactly. In the case of convex objective function and linear constraints, a...

We introduce the smoothed analysis of algorithms, which continuously interpolates between the worst-case and average-case analyses of algorithms. In smoothed analysis, we measure the maximum over inputs of the expected performance of an algorithm under small random perturbations of that input. We measure this performance in terms of both the input size and the magnitude of the perturbations. We...

We introduce the smoothed analysis of algorithms, which is a hybrid of the worst-case and average-case analysis of algorithms. In smoothed analysis, we measure the maximum over inputs of the expected performance of an algorithm under small random perturbations of that input. We measure this performance in terms of both the input size and the magnitude of the perturbations. We show that the simp...

We introduce the smoothed analysis of algorithms, which is a hybrid of the worst-case and average-case analysis of algorithms. In smoothed analysis, we measure the maximum over inputs of the expected performance of an algorithm under small random perturbations of that input. We measure this performance in terms of both the input size and the magnitude of the perturbations. We show that the simp...