Sampling Criteria for Nyström Method

Nyström Sampling Depends on the Eigenspec- Trum Shape of the Data

Spectral clustering has shown a superior performance in analyzing the cluster structure. However, its computational complexity limits its application in analyzing large-scale data. To address this problem, many low-rank matrix approximating algorithms are proposed, including the Nyström method – an approach with proven approximate error bounds. There are several algorithms that provide recipes ...

Improving CUR Matrix Decomposition and Nyström Approximation via Adaptive Sampling

The CUR matrix decomposition and Nyström method are two important low-rank matrix approximation techniques. The Nyström method approximates a positive semidefinite matrix in terms of a small number of its columns, while CUR approximates an arbitrary data matrix by a small number of its columns and rows. Thus, the CUR decomposition can be regarded as an extension of the Nyström method. In this p...

An Embedded 4(3) Pair of Explicit Trigonometrically-Fitted Runge-Kutta-Nyström Method for Solving Periodic Initial Value Problems

A Zero-Dissipative Runge-Kutta-Nyström Method with Minimal Phase-Lag

An explicit Runge-Kutta-Nyström method is developed for solving second-order differential equations of the form q′′ f t, q where the solutions are oscillatory. The method has zero-dissipation with minimal phase-lag at a cost of three-function evaluations per step of integration. Numerical comparisons with RKN3HS, RKN3V, RKN4G, and RKN4C methods show the preciseness and effectiveness of the meth...

Stability of Runge–Kutta–Nyström methods

In this paper, a general and detailed study of linear stability of Runge–Kutta–Nyström (RKN) methods is given. In the case that arbitrarily stiff problems are integrated, we establish a condition that RKN methods must satisfy so that a uniform bound for stability can be achieved. This condition is not satisfied by any method in the literature. Therefore, a stable method is constructed and some ...