P-stable general Nyström methods fory″=f(y(t))

Sampling Methods for the Nyström Method

The Nyström method is an efficient technique to generate low-rank matrix approximations and is used in several large-scale learning applications. A key aspect of this method is the procedure according to which columns are sampled from the original matrix. In this work, we explore the efficacy of a variety of fixed and adaptive sampling schemes. We also propose a family of ensemble-based samplin...

Theoretical analysis of Sinc-Nyström methods for Volterra integral equations

Runge-Kutta-Nyström-type parallel block predictor-corrector methods

This paper describes the construction of block predictor-corrector methods based on Runge-Kutta-Nystrr om correctors. Our approach is to apply the predictor-corrector method not only with stepsize h, but, in addition (and simultaneously) with stepsizes a i h; i = 1; : : :; r. In this way, at each step, a whole block of approximations to the exact solution at oo-step points is computed. In the n...

Optimal Rates for Learning with Nyström Stochastic Gradient Methods

In the setting of nonparametric regression, we propose and study a combination of stochastic gradient methods with Nyström subsampling, allowing multiple passes over the data and mini-batches. Generalization error bounds for the studied algorithm are provided. Particularly, optimal learning rates are derived considering different possible choices of the step-size, the mini-batch size, the numbe...

A review of Nyström methods for large-scale machine learning

Generating a low-rank matrix approximation is very important in large-scale machine learning applications. The standard Nyström method is one of the state-of-the-art techniques to generate such an approximation. It has got rapid developments since being applied to Gaussian process regression. Several enhanced Nyström methods such as ensemble Nyström, modified Nyström and SS-Nyström have been pr...