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Near Extensions and Alignment of Data in R(superscript)n
book

Near Extensions and Alignment of Data in R(superscript)n

by Steven B. Damelin
November 2023
Intermediate to advanced content levelIntermediate to advanced
192 pages
3h 29m
English
Wiley
Content preview from Near Extensions and Alignment of Data in R(superscript)n

14 Extensions of Smooth Small Distortions: First Results

Lemma 14.1. Let upper B left-parenthesis z comma r right-parenthesis subset-of upper E. Then there exists a Euclidean motion upper A, such that for every upper L greater-than-or-equal-to 1, and for every

(14.1) y element-of upper B left-parenthesis z comma upper L r right-parenthesis intersection upper E comma we have StartAbsoluteValue phi left-parenthesis y right-parenthesis minus upper A left-parenthesis y right-parenthesis EndAbsoluteValue less-than-or-equal-to upper C upper L squared epsilon r period

Proof. Without loss of generality, we may assume z = 0, r = 1, and phi left-parenthesis 0 right-parenthesis = 0. Let e 1 comma ellipsis comma e Subscript n Baseline be the unit vector in double-struck upper R Superscript n. We have for each , and for . Since , it ...

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Publisher Resources

ISBN: 9781394196777Purchase Link