abbdd278_Es___Numerical_Methods_Seminar__TITLE
[DATE] 03/13/06 [SPEAKER] Hennie Poulisse Shell [TITLE] 
TITLE: Best Approximation in an Inner Product Space from the Range of a Linear Operator over a Polyhedron with an Application to Oil Production SPEAKER: Hennie Poulisse ABSTRACT: The range of the linear operator over a polyhedron considered in this paper is a convex subset H of a finite dimensional subspace S of the ambient inner product space X. According to the reduction principle the best approximation to a point of X from H equals the best approximation to the best approximation to that point of X from S from H. Equivalent representations are given for H in terms of ^�opposite^� translated convex cones. Moreover translated polar cones are introduced. Subsequently, explicit calculations are given for the best approximations from a translated convex cone and from a translated polar cone. Using the Boyle-Dykstra theorem, these results are used to give a constructive proof of the best approximation to a point of X from H. The result is finally applied to real-life data from oil industry in that a solution is presented for a very important problem in oil - and gas production operations called the reconciliation problem, where the contribution of individual wells to a measured total production has to be assessed.
CCMA PDEs & Numerical Methods Seminar
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