The overlap Dirac operator at nonzero quark chemical potential involves the computation of the sign function of a non-Hermitian matrix. In this talk we present an iterative method, first proposed by us in Ref. [1], which allows for an efficient computation of the operator, even on large lattices. The starting point is a Krylov subspace approximation, based on the Arnoldi algorithm, for the eval...

The rational Krylov sequence (RKS) method can be seen as a generalisation of Arnoldi’s method. It projects a matrix pencil onto a smaller subspace; this projection results in a small upper Hessenberg pencil. As for the Arnoldi method, RKS can be restarted implicitly, using the QR decomposition of a Hessenberg matrix. This restart comes with a projection of the subspace using a rational function...

Standard subspace methods for the identification of discrete-time, linear, time-invariant systems are transformed into generalized convex optimization problems in which the poles of the system estimate are constrained to lie within user-defined convex regions of the complex plane. The transformation is done by restating subspace methods such as the minimization of a Frobenius norm affine in the...

The spatio-temporal-prediction (STP) method for multichannel speech enhancement has recently been proposed. This approach makes it theoretically possible to attenuate the residual noise without distorting speech. In addition, the STP method depends only on the second-order statistics and can be implemented using a simple linear filtering framework. Unfortunately, some numerical problems can ari...

Recently, R-dimensional subspace-based parameter estimation techniques have been improved by exploiting the tensor structure already in the subspace estimation step via a Higher Order Singular Value Decompostion (HOSVD) based low-rank approximation. Often this parameter estimation is performed in the presence of colored noise or interference, which can severely degrade the estimation accuracy. ...

Sketching is a powerful dimensionality reduction tool for accelerating statistical learning algorithms. However, its applicability has been limited to a certain extent since the crucial ingredient, the so-called oblivious subspace embedding, can only be applied to data spaces with an explicit representation as the column span or row span of a matrix, while in many settings learning is done in a...

The pseudospectral abscissa and the stability radius are well-established tools for quantifying the stability of a matrix under unstructured perturbations. Based on first-order eigenvalue expansions, Guglielmi and Overton [SIAM J. Matrix Anal. Appl., 32 (2011), pp. 1166-1192] recently proposed a linearly converging iterative method for computing the pseudospectral abscissa. In this paper, we pr...

Multibody motion segmentation is important in many computer vision tasks. This paper presents a novel spectral clustering approach to motion segmentation based on motion trajectory. We introduce a new affinity matrix based on the motion trajectory and map the feature points into a low dimensional subspace. The feature points are clustered in this subspace using a graph spectral approach. By com...

The aim of this paper is to indicate and explore the similarities between three different subspace algorithms for the identification of combined deterministic-stochastic systems. The similarities between these algorithms have been obscured, due to different notations and backgrounds. It is shown that all three algorithms are special cases of one unifying theorem. The comparison also reveals tha...