Scholarlink

<p>In this paper, we address the Hermite interpolation problem on the space of probability measures <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {P}_{+}(I)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">P</mi> <mo>+</mo> </msub> <mrow> <mo stretchy="false">(</mo> <mi>I</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> equipped with a Hilbert manifold structure. We derive explicit theoretical expressions for fundamental geometric structures on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {P}_{+}(I)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">P</mi> <mo>+</mo> </msub> <mrow> <mo stretchy="false">(</mo> <mi>I</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, including the Levi-Civita connection, minimal geodesics, parallel transport, the exponential map, and the logarithm map. The Hermite interpolation spline is then constructed by extending the classical Hermite interpolation framework through these geodesic operations.</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

Cubic Hermite Splines on the Hilbert manifold of Probability Measures

  • 期刊论文

  • 发表日期：

    2026年1月20日

查看全文
  • Ines Adouani

摘要

In this paper, we address the Hermite interpolation problem on the space of probability measures \(\mathcal {P}_{+}(I)\) P + ( I ) equipped with a Hilbert manifold structure. We derive explicit theoretical expressions for fundamental geometric structures on \(\mathcal {P}_{+}(I)\) P + ( I ) , including the Levi-Civita connection, minimal geodesics, parallel transport, the exponential map, and the logarithm map. The Hermite interpolation spline is then constructed by extending the classical Hermite interpolation framework through these geodesic operations.