When the computation of efficient preconditioners for individual linear systems of a sequence is expensive, significant reduction of costs can be achieved by updating previous preconditioners. For large and sparse systems, this has been done, among others, by recycling subspaces when using a Krylov subspace method [3], by means of small rank updates when applying Quasi-Newton methods [2] or wit...

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...

Let A be a subspace arrangement and let (A; t) be the characteristic polynomial of its intersection lattice L(A). We show that if the subspaces in A are taken from L(Bn), where Bn is the type B Weyl arrangement, then (A; t) counts a certain set of lattice points. This is the only known combinatorial interpretation of this polynomial in the subspace case. One can use this result to study the par...

In this paper, we construct a lagrangian subspace of the space of representations Mg,l := HomC(πg,l, U)/U of the fundamental group πg,l of a punctured Riemann surface into an arbitrary compact connected Lie group U . This lagrangian subspace is obtained as the fixed-point set of an anti-symplectic involution β̂ defined on Mg,l. We show that the involution β̂ is induced by a form-reversing involut...

The algebraic structure on the subspace of the quasi-primary vectors given by the projection of the (n) products of a conformal superalgebra is formulated. As an application the complete list of simple physical conformal superalgebras is given. The list contains a one-parameter family of superconformal algebras with 4 supercharges that is simple for general values.

For effective retrieval of visual information, statistical learning plays a pivotal role. Statistical learning in such a context faces at least two major mathematical challenges: scarcity of training data, and imbalance of training classes. We present these challenges and outline our methods for addressing them: active learning, recursive subspace co-training, adaptive dimensionality reduction,...

This work is inspired by a paper of Hertel and Pott on maximum non-linear functions [8]. Geometrically, these functions correspond with quasi-quadrics; objects introduced in [5]. Hertel and Pott obtain a characterization of some binary quasi-quadrics in a ne spaces by their intersection numbers with hyperplanes and spaces of codimension 2. We obtain a similar characterization for quadrics in pr...

The application of state-space-based subspace system identification methods to training-based estimation for quasi-static multiinput–multi-output (MIMO) frequency-selective channels is explored with the motivation for better model approximation performance. A modification of the traditional subspace methods is derived to suit the non-contiguous nature of training data in mobile communication sy...

We use the Schmidt Subspace Theorem to establish the transcendence of a class of quasi-periodic continued fractions. This improves earlier works of Maillet and of A. Baker. We also improve an old result of Davenport and Roth on the rate of increase of the denominators of the convergents to any real algebraic number.

The Computational Singular Perturbation (CSP) method of simplified kinetics modeling is presented with emphasis on its comparative merits versus conventional methodologies. A new “refinement” procedure for the basis vectors spanning the fast reaction subspace is presented. A simple example is first worked through using the conventional partial-equilibrium and quasi-steady approximations, and is...