The linear discriminant analysis based on the generalized singular value decomposition (LDA/GSVD) has recently been introduced to circumvents the nonsingularity restriction that occur in the classical LDA so that a dimension reducing transformation can be effectively obtained for undersampled problems. In this paper, relationships between support vector machines (SVMs) and the generalized linea...

A new star pattern recognition method is developed using singular value decomposition of a measured unit column vector matrix in a measurement frame and the corresponding cataloged vector matrix in a reference frame. It is shown that singular values and right singular vectors are invariant with respect to coordinate transformation and robust under uncertainty. One advantage of singular value co...

We construct unbounded strange attractors for vector fields in R that are robust transitive under uniformly small perturbations. Their geometry is reminiscent of geometric Lorenz and other singular hyperbolic attractors, but they contain no equilibria.

We show that Horrocks' criterion for the splitting of rank two vector bundles in P 3 can be extended, with some assumptions on the Chern classes, on non singular hypersurfaces in P 4. Extension of other splitting criterions are studied.

We show that Horrocks' criterion for the splitting of rank two vector bundles in P 3 can be extended, with some assumptions on the Chern classes, on non singular hypersurfaces in P 4. Extension of other splitting criterions are studied.

We confirm a conjecture of Bernstein-Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.

A standard way of dealing with a regular matrix polynomial P (λ) is to convert it into an equivalent matrix pencil – a process known as linearization. Two vector spaces of pencils L1(P ) and L2(P ) that generalize the first and second companion forms have recently been introduced by Mackey, Mackey, Mehl and Mehrmann. Almost all of these pencils are linearizations for P (λ) when P is regular. Th...

It is shown that the singular set for the Yang-Mills flow on unstable holomorphic vector bundles over compact Kähler manifolds is completely determined by the Harder-NarasimhanSeshadri filtration of the initial holomorphic bundle. We assign a multiplicity to irreducible top dimensional components of the singular set of a holomorphic bundle with a filtration by saturated subsheaves. We derive a ...

This paper presents an O(n2 log n) algorithm for computing the symmetric singular value decomposition of square Hankel matrices of order n, in contrast with existing O(n3) SVD algorithms. The algorithm consists of two stages: first, a complex square Hankel matrix is reduced to a complex symmetric tridiagonal matrix using the block Lanczos method in O(n2 log n) flops; second, the singular values...