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This Chapter is devoted to the theoretical foundation of approximate quasi-interpolation. In Sect. 2.1, we introduce notation and mention basic results, which will be used throughout the book. Error estimations of general approximate quasi-interpolants in uniform and integral norms are obtained in Sects. 2.2, 2.3 and 2.4. In Sect. 2.5, we formulate conditions on the generating functions, which ensure high-order approximations up to a prescribed precision. We provide examples of generating functions which generate approximate quasi-interpolants of order N up to a small saturation error.

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Quasi-interpolation

  • 章节

  • 发表日期：

    2025年

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  • Flavia Lanzara,
  • Vladimir Maz’ya,
  • Gunther Schmidt

摘要

This Chapter is devoted to the theoretical foundation of approximate quasi-interpolation. In Sect. 2.1, we introduce notation and mention basic results, which will be used throughout the book. Error estimations of general approximate quasi-interpolants in uniform and integral norms are obtained in Sects. 2.2, 2.3 and 2.4. In Sect. 2.5, we formulate conditions on the generating functions, which ensure high-order approximations up to a prescribed precision. We provide examples of generating functions which generate approximate quasi-interpolants of order N up to a small saturation error.