We study two applications of standard Gaussian random multipliers. At first we prove that with a probability close to 1 such a multiplier is expected to numerically stabilize Gaussian elimination with no pivoting as well as block Gaussian elimination. Then, by extending our analysis, we prove that such a multiplier is also expected to support low-rank approximation of a matrix without customary...

In Gaussian elimination it is often desirable to preserve existing zeros (sparsity). This is closely related to perfect elimination schemes on graphs. Such schemes can be found in polynomial time. Gaussian elimination uses a pivot for each column, so opportunities for preserving sparsity can be missed. In this paper we consider a more flexible process that selects a pivot for each nonzero to be...

For many applied problems in the context of clustering via mixture models, the estimates of the component means and covariance matrices can be affected by observations that are atypical of the components in the mixture model being fitted. In this paper, we consider for Gaussian mixtures a robust estimation procedure using multiresolution kd-trees. The method provides a fast EM-based approach to...

We consider Volterra Gaussian processes on [0, T ], where T > 0 is a fixed time horizon. These are processes of type Xt = R t 0 zX(t, s)dWs, t ∈ [0, T ], where zX is a square-integrable kernel, and W is a standard Brownian motion. An example is fractional Brownian motion. By using classical techniques from operator theory, we derive measure-preserving transformations of X, and their inherently ...

This paper introduces a redundant localisation system, combining a low-cost Gaussian pose tracker and a particle filter localiser which is more CPU intensive. Ideally, the Gaussian pose tracker can be used for most of the time and the particle filter localiser switched on only when the Gaussian pose tracker fails. The problem studied here is to determine when the Gaussian pose tracker has faile...

We propose a method for post-processing an ensemble of multivariate forecasts in order to obtain a joint predictive distribution of weather. Our method utilizes existing univariate postprocessing techniques, in this case ensemble Bayesian model averaging (BMA), to obtain estimated marginal distributions. However, implementing these methods individually offers no information regarding the joint ...

Abstract. Traditionally, transfer functions have been designed manually for each operation in a program, instruction by instruction. In such a setting, a transfer function describes the semantics of a single instruction, detailing how a given abstract input state is mapped to an abstract output state. The net effect of a sequence of instructions, a basic block, can then be calculated by composi...