Good, Better, and Best Meshes in Piecewise Linear Interpolation

摘要

We first describe the good meshes obtained by C. deBoor which roughlyequidistribute the classical error bound in piecewise linear interpolation. We then proceed to obtain better meshes which more precisely equidistribute this bound. Finally, we obtain meshes which equidistribute the maximum absolute error (not bound) and refer to these meshes as best. Some graphical results are then presented comparing these three types of meshes.