Abstract

. Recently several algorithms have been given for obtaining piecewise linear (PL) approximations of manifolds M which are implicitly defined. We derive error estimates and global approximation results for such algorithms. 1. Introduction Recently several algorithms have been given for obtaining piecewise linear (PL) approximations of manifolds M which are implicitly defined as a solution set of an equation H(x) = 0, where 0 # range H and H :IR N+K # IR N is a smooth map. In this paper we derive error estimates and global approximation results for the algorithms given in [2] and [5]. Analogous results can also be obtained for the algorithms given in [3] and [7]. Many of the given error estimates have been obtained by Saigal[8] for the case K = 0. However for K>0, the proofs need a di#erent approach. Although our assumptions can be relaxed in several ways, we make them here in order to hold our discussion to a simple and unified form. Specifically we assume that 0 is a regular v...

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