Conceitos Básicos
Radial basis function interpolation with improved error bounds can be achieved by utilizing a conditionally positive definite function of order m.
Resumo
The content discusses the application of radial basis function (RBF) interpolation using a conditionally positive definite function of order m. It explores the concept of doubling convergence rates for functions in smoother normed spaces, providing insights into numerical analysis and approximation theory.
Abstract:
- Convergence rates for L2 approximation in Hilbert space H are crucial in numerical analysis.
- Doubling convergence rate for functions in smoother normed space B compared to general rate in native space H.
Introduction:
- Approximating real-valued function f on domain D using H-orthogonal projection Pf onto subspace V ⊂H.
- Aim to provide improved error bounds for functions g in smoother normed space B embedded in H.
Data Extraction:
- "Convergence rates for L2 approximation in Hilbert space H are crucial in numerical analysis."
- "Doubling convergence rate for functions in smoother normed space B compared to general rate in native space H."
Estatísticas
収束率の重要性を考えると、数値解析においてHilbert空間HでのL2近似の収束率は重要です。
一般的なレートと比較して、より滑らかな規範空間B内の関数の収束率を倍増させます。