88,223 research outputs found
Pruning Algorithms for Pretropisms of Newton Polytopes
Pretropisms are candidates for the leading exponents of Puiseux series that
represent solutions of polynomial systems. To find pretropisms, we propose an
exact gift wrapping algorithm to prune the tree of edges of a tuple of Newton
polytopes. We prefer exact arithmetic not only because of the exact input and
the degrees of the output, but because of the often unpredictable growth of the
coordinates in the face normals, even for polytopes in generic position. We
provide experimental results with our preliminary implementation in Sage that
compare favorably with the pruning method that relies only on cone
intersections.Comment: exact, gift wrapping, Newton polytope, pretropism, tree pruning,
accepted for presentation at Computer Algebra in Scientific Computing, CASC
201
Computability and analysis: the legacy of Alan Turing
We discuss the legacy of Alan Turing and his impact on computability and
analysis.Comment: 49 page
Direct numerical simulation of turbulence on a Connection Machine CM-5
In this paper we report on our first experiences with direct numerical simulation of turbulent flow on a 16-node Connection Machine CM-5. The CM-5 has been programmed at a global level using data parallel Fortran. A two-dimensional direct simulation, where the pressure is solved using a Conjugate Gradient method without preconditioning, runs at 23% of the peak. Due to higher communication costs, 3D simulations run at 13% of the peak. A diagonalwise re-ordered Incomplete Choleski Conjugate Gradient method cannot compete with a standard CG-method on the CM-5.
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