Scholarlink

<p>This paper begins by reviewing numerous theoretical advancements in the field of multivariate splines, primarily contributed by Professor Larry L. Schumaker. These foundational results have enabled numerous applications and computational methods. It then highlights various practical applications of multivariate splines. Typical applications include scattered data fitting and interpolation, the construction of smooth curves and surfaces, and the numerical solutions of various partial differential equations, encompassing both linear and nonlinear PDEs over domains with curved boundaries. In addition to these established uses, the paper introduces a novel application of multivariate splines for function value denoising. This innovative approach facilitates the creation of LKB splines, which are instrumental in approximating high-dimensional functions and effectively circumventing the curse of dimensionality.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Multivariate splines and their applications

  • 期刊论文

  • 发表日期：

    2025年7月28日

查看全文
  • Ming-Jun Lai

摘要

This paper begins by reviewing numerous theoretical advancements in the field of multivariate splines, primarily contributed by Professor Larry L. Schumaker. These foundational results have enabled numerous applications and computational methods. It then highlights various practical applications of multivariate splines. Typical applications include scattered data fitting and interpolation, the construction of smooth curves and surfaces, and the numerical solutions of various partial differential equations, encompassing both linear and nonlinear PDEs over domains with curved boundaries. In addition to these established uses, the paper introduces a novel application of multivariate splines for function value denoising. This innovative approach facilitates the creation of LKB splines, which are instrumental in approximating high-dimensional functions and effectively circumventing the curse of dimensionality.