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Excerpt from Optimal Iterative Refinement Methods We assume that all the elements are shape regular in the sense that there is a uniform bound on hk/pk. Here hk and pk are the diameter and the radius of the largest inscribed sphere of any element K, respectively. Our bounds in the theory developed below also depend on the shape of the subregions Q, . Thus in order for our proofs to work, we cannot allow the sets \qi to become arbitrarily thin in comparison with the diameter of Q, _1. We also assume that the area of any triangle on level i can be bounded by const. Qj'i, j i times the area of the triangle on level j of which it is a part. Here q is a constant 1. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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