A sequence ${T_n}_{n=1}^{infty}$ of bounded linear  operators on a separable infinite dimensional Hilbert space $mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $Msubseteq mathcal{H},$ if there exists a vector $xin mathcal{H}$ such that the disk-scaled orbit ${alpha T_n x: nin mathbb{N}, alpha inmathbb{C}, | alpha | leq 1}cap M$ is dense in $M$. The goal of t...

Pipelined Krylov methods seek to ameliorate the latency due to inner products necessary for projection by overlapping it with the computation associated with sparse matrix-vector multiplication. We clarify a folk theorem that this can only result in a speedup of 2× over the naive implementation. Examining many repeated runs, we show that stochastic noise also contributes to the latency, and we ...

Recent computational and theoretical studies have shown that the matrix-vector product occurring at each step of a Krylov subspace method can be relaxed as the iterations proceed, i.e., it can be computed in a less exact manner, without degradation of the overall performance. In the present paper a general operator treatment of this phenomenon is provided and a new result further explaining its...

Cramér-Rao bounds on estimation accuracy are established for estimation problems on arbitrary manifolds in which no set of intrinsic coordinates exists. The frequently encountered examples of estimating either an unknown subspace or a covariance matrix are examined in detail. The set of subspaces, called the Grassmann manifold, and the set of covariance (positive-definite Hermitian) matrices ha...

This paper provides a comprehensive framework for the state-space approach to Boolean networks. First, it surveys the authors' recent work on the topic: Using semitensor product of matrices and the matrix expression of logic, the logical dynamic equations of Boolean (control) networks can be converted into standard discrete-time dynamics. To use the state-space approach, the state space and its...

Recent frequency domain identiication algorithms based on subspace based techniques are discussed. The algorithms construct a state-space model by means of extraction of the signal subspace from a matrix constructed from frequency data. A singular value decomposition plays a key part in the subspace extraction. The subspace methods are non-iterative methods in contrast to classical iterative pa...

Principal Components Analysis (PCA) is one of the most widely used dimension reduction techniques. Given a matrix of clean data, PCA is easily accomplished via singular value decomposition (SVD) on the data matrix. While PCA for relatively clean data is an easy and solved problem, it becomes much harder if the data is corrupted by even a few outliers. The reason is that SVD is sensitive to outl...

The art of visual tracking has been widely studied in the past decades [6]. While most of researches focus on exploring new methods to represent object appearance, little attention has been paid on the description of object motion. In this paper we propose a novel motion model for visual tracking, and in comparison with previous methods, it can better parameterize instantaneous image motion cau...

A formula for the distance of a Toeplitz matrix to the subspace of {e}-circulant matrices is presented, and applications of {e}-circulant matrices to preconditioning of linear systems of equations with a Toeplitz matrix are discussed. Copyright c © 2006 John Wiley & Sons, Ltd. key words: Toeplitz matrix, circulant matrix, {e}-circulant, matrix nearness problem, distance to normality, preconditi...