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Constrained optimization in classes of analytic functions with prescribed pointwise values

Laurent Baratchart 1 Juliette Leblond 1 Dmitry Ponomarev 1, *
* Corresponding author
Abstract : We consider an overdetermined problem for Laplace equation on a disk with partial boundary data where additional pointwise data inside the disk have to be taken into account. After reformulation, this ill-posed problem reduces to a bounded extremal problem of best norm-constrained approximation of partial L2 boundary data by traces of holomorphic functions which satisfy given pointwise interpolation conditions. The problem of best norm-constrained approximation of a given L2 function on a subset of the circle by the trace of a H2 function has been considered in [Baratchart & Leblond, 1998]. In the present work, we extend such a formulation to the case where the additional interpolation conditions are imposed. We also obtain some new results that can be applied to the original problem: we carry out stability analysis and propose a novel method of evaluation of the approximation and blow-up rates of the solution in terms of a Lagrange parameter leading to a highly-efficient computational algorithm for solving the problem.
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https://hal.inria.fr/hal-00938491
Contributor : Dmitry Ponomarev <>
Submitted on : Thursday, August 13, 2015 - 6:02:40 PM
Last modification on : Thursday, February 7, 2019 - 4:52:24 PM
Document(s) archivé(s) le : Saturday, November 14, 2015 - 10:34:08 AM

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  • HAL Id : hal-00938491, version 4
  • ARXIV : 1401.7633

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Laurent Baratchart, Juliette Leblond, Dmitry Ponomarev. Constrained optimization in classes of analytic functions with prescribed pointwise values. [Research Report] RR-8459, INRIA Sophia Antipolis - Méditerranée; INRIA. 2014. ⟨hal-00938491v4⟩

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