A new and sharper bound for Legendre expansion of differentiable functions
arXiv:1803.0033628 citationsh-index: 15
AI Analysis
Provides a tighter theoretical bound for Legendre approximation, relevant to numerical analysis and approximation theory.
The paper derives a sharper bound for Legendre coefficients of differentiable functions and a new uniform error bound for truncated Legendre series, with an example demonstrating sharpness.
In this paper, we provide a new and sharper bound for the Legendre coefficients of differentiable functions and then derive a new error bound of the truncated Legendre series in the uniform norm. The key idea of proof relies on integration by parts and a sharp Bernstein-type inequality for the Legendre polynomial. An illustrative example is provided to demonstrate the sharpness of our new results.