Polygonal Approximation 3
- Author:
- Ryan Hirst
- Topic:
- Equations
An improvement to the Polygonal Method:
Consider segment PR, joining two consecutive points in the original approximation.
Find y' at the midpoint Q of PR.
Draw a line through P with this slope, and mark off an improved approximation R' to replace R.
This is equivalent to using the third term (second derivative) in the Taylor series expansion.
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Polygonal Approximation:
1. Step-by-step construction http://www.geogebratube.org/material/show/id/27865
2. Transfer the procedure to the Spreadsheet view: http://www.geogebratube.org/material/show/id/27754
*3. Improvement: Add a term in the Taylor expansion*
4. Comparison, and corrector formulas: http://www.geogebratube.org/material/show/id/29107