| Event Description:
John Boyd, Department of Atmospheric, Oceanic and Space Science, University of Michigan Exponentially accurate Rung-free approximation from samples on an evenly-spaced grid for non-periodic functions Approximating a function from its values at a f(xi) set of evenly spaced points xi through (N+1)-point polynomial interpolation often fails because of divergence near the endpoints, the 鈥榬unge Phenomenon鈥�. The present study shows how to achieve an error that decreases exponentially fast with N. Normalizing the span of the points to [-1, 1], the new strategy applies a filtered trigonometric interpolant on the subinterval [-1+D, 1-D] and ordinary polynomial interpolation in these two remaining subintervals. Convergence is guaranteed because the width D of the polynomial interpolation intervals decreases as N鈫掆垶, being proportional to 1/N. Applications to Gibbs Phenomenon and hydrodynamic shocks are discussed. |
| Location Information: 听听() 1111 Engineering DR聽 Boulder, CO聽 搁辞辞尘:听265 |
| Contact Information: Name: Ian Cunningham Phone: 303-492-4668 贰尘补颈濒:听amassist@colorado.edu |