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In this paper, we present a numerical scheme to select the kernel shape parameters within partition of unity methods. In an interpolation framework, we propose the use of a leave-one-out cross validation technique combined with efficient global optimization tools from the class of Lipschitz derivative-free methods. Numerical results highlight how this union is generally able to produce some enhancements in terms of both efficiency and accuracy.

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Choosing Kernel Shape Parameters in Partition of Unity Methods by Univariate Global Optimization Techniques

  • 会议论文

  • 发表日期：

    2025年

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  • Roberto Cavoretto,
  • Alessandra De Rossi,
  • Yaroslav D. Sergeyev

摘要

In this paper, we present a numerical scheme to select the kernel shape parameters within partition of unity methods. In an interpolation framework, we propose the use of a leave-one-out cross validation technique combined with efficient global optimization tools from the class of Lipschitz derivative-free methods. Numerical results highlight how this union is generally able to produce some enhancements in terms of both efficiency and accuracy.