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Edwin Powell Hubble

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A multivariate Powell-Sabin interpolant

We consider the problem of constructing a C1 piecewise quadratic interpolant, Q, to positional and gradient data defined at the vertices of a tessellation of n-simplices in IR. The key to the interpolation scheme is to appropriately subdivide each simplex to ensure that certain necessary geometric constraints are satisfied by the subdivision points. We establish these constraints using the Bern...

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Convergence Properties of Beale - Powell

The Beale-Powell restart algorithm is highly useful for large-scale unconstrained optimization. In this paper, we use an example to show that the algorithm may fail to converge. The global convergence of a slightly modiied algorithm is proved.