10,227 research outputs found
On embeddings of homogeneous spaces with small boundary
We study equivariant embeddings with small boundary of a given homogeneous
space , where is a connected, linear algebraic group with trivial
Picard group and only trivial characters, and is an extension of
a connected Grosshans subgroup by a torus. Under certain maximality conditions,
like completeness, we obtain finiteness of the number of isomorphism classes of
such embeddings, and we provide a combinatorial description the embbeddings and
their morphisms. The latter allows a systematic treatment of examples and basic
statements on the geometry of the equivariant embeddings of a given homogeneous
space .Comment: minor changes, 30 pages, to appear in J. Algebr
Adapting the interior point method for the solution of LPs on serial, coarse grain parallel and massively parallel computers
In this paper we describe a unified scheme for implementing an interior point algorithm (IPM) over a range of computer architectures. In the inner iteration of the IPM a search direction is computed using Newton's method. Computationally this involves solving a sparse symmetric positive definite (SSPD) system of equations. The choice of direct and indirect methods for the solution of this system, and the design of data structures to take advantage of serial, coarse grain parallel and massively parallel computer architectures, are considered in detail. We put forward arguments as to why integration of the system within a sparse simplex solver is important and outline how the system is designed to achieve this integration
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