Many physical problems are naturally formulated as nonlinear par-abolic systems of partial diierential equations in periodic geometry. In this paper, a simple, eecient, spectrally-accurate numerical method for these problems is described and implemented. The method combines stii extrapolation with fast solvers for elliptic systems. Theory and numerical results show that the method solves even d...

The application of spectral methods to the software clustering problem has the advantage of producing results that are within a known factor of the optimal solution. Heuristic search methods, such as those supported by the Bunch clustering tool, only guarantee local optimality which may be far from the global optimum. In this paper, we apply the spectral methods to the software clustering probl...

Supervised topic models simultaneously model the latent topic structure of large collections of documents and a response variable associated with each document. Existing inference methods are based on either variational approximation or Monte Carlo sampling. This paper presents a novel spectral decomposition algorithm to recover the parameters of supervised latent Dirichlet allocation (sLDA) mo...

Given a network of nodes, minimizing the spread of a contagion using a limited budget is a well-studied problem with applications in network security, viral marketing, social networks, and public health. In real graphs, virus may infect a node which in turn infects its neighbor nodes and this may trigger an epidemic in the whole graph. The goal thus is to select the best k nodes (budget constra...

Last time, we talked about spectral ranking methods, and we observed that they can be computed as eigenvectors of certain matrices or as the solution to systems of linear equations of certain constraint matrices. These computations can be performed with a black box solver, but they can also be done with specialized solvers that take advantage of the special structure of these matrices. (For exa...

This is the second in a series of papers on the numerical treatment of hyperelliptic theta-functions with spectral methods. A code for the numerical evaluation of solutions to the Ernst equation on hyperelliptic surfaces of genus 2 is extended to arbitrary genus and general position of the branch points. The use of spectral approximations allows for an efficient calculation of all characteristi...

In this paper we show that a large class of regularization methods designed for solving ill-posed inverse problems gives rise to novel learning algorithms. All these algorithms are consistent kernel methods which can be easily implemented. The intuition behind our approach is that, by looking at regularization from a filter function perspective, filtering out undesired components of the target ...

Krylov subspace spectral methods have been shown to be high-order accurate in time and more stable than explicit time-stepping methods, but also more difficult to implement efficiently. This paper describes how these methods can be fashioned into practical solvers by exploiting the simple structure of differential operators Numerical results concerning accuracy and efficiency are presented for ...

In recent years it has been made more and more clear that the critical issue in gradient methods is the choice of the step length, whereas using the gradient as search direction may lead to very effective algorithms, whose surprising behaviour has been only partially explained, mostly in terms of the spectrum of the Hessian matrix. On the other hand, the convergence of the classical Cauchy stee...

Dynamic functional imaging experiments typically generate large, multivariate data sets that contain considerable spatial and temporal complexity. The goal of this introduction is to present signal-processing techniques that allow the underlying spatiotemporal structure to be readily distilled and that also enable signal versus noise contributions to be separated.