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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

2 Building ε-distortions: Slow Twists, Slides

In this chapter, we introduce a key object in the near distorted Whitney extension problem, we call a epsilon-distorted diffeomorphisim which distorts distances by factors 1 plus epsilon and 1 minus epsilon where epsilon greater-than 0 is small enough. We introduce two examples of these maps, we call Slow Twists and Slides. We look at their actions and how they can be used to construct epsilon-distorted diffeomorphisims which agree with Euclidean motions in double-struck upper R Superscript d. [39, 67]

We now begin to look at Problem 1 and Problem 2. We will translate “smooth” into the idea of a c-distorted diffeomorphism (See Figures 2.12.12).

Figure 2.1 Initial points lying on the line , and the application of a Slow Twist with , with (top ...

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ISBN: 9781394196777Purchase Link