Two-sided estimation of diameters reduction rate for the longest edge n-section of triangles with n⩾4

In this work we study the diameters reduction rate for the iterative application of the longest edge (LE) n-section of triangles for n⩾4. The maximum diameter dkn of all triangles generated at the kth iteration of the LE n-section is closely connected with the properties of the triangular mesh generated by this refinement scheme. The upper and the lower bounds for dk2 were proved by Kearfott in [9] and for dk3 by Plaza et al. [12]. Here, we derive the two-sided estimates for dkn with n⩾4.