On Piecewise Linear Approximations to Smooth Mappings

1 May 1979

journal article
Published by Institute for Operations Research and the Management Sciences (INFORMS) in Mathematics of Operations Research

Vol. 4 (2) , 153-161
https://doi.org/10.1287/moor.4.2.153

Abstract

Given a continuously differentiable mapping f from Rⁿ into Rⁿ, in this work we study piecewise linear approximations to it on certain subdivisions of Rⁿ. It is shown that several properties of the subdivision are critical when the Jacobians of the pieces of linearity of the approximation are required to be close to the Jacobians of f. In addition, it is shown that even under arbitrary scaling of the triangulations used in fixed point algorithms, good approximations of the derivatives result.

Keywords

DIFFERENTIABLE
PIECEWISE LINEAR
LINEAR APPROXIMATIONS
JACOBIANS
GOOD
SMOOTH
TRIANGULATIONS
PIECES
ARBITRARY

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