gibson:teaching:fall-2016:math753:lagrangepoly
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gibson:teaching:fall-2016:math753:lagrangepoly [2016/11/11 12:34] gibson |
gibson:teaching:fall-2016:math753:lagrangepoly [2016/11/11 12:39] (current) gibson |
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| P(x) = 4 \frac{(x-1)(x-2)}{(-1)(-2)} + 3 \frac{(x)(x-2)}{(1)(-1)} + 6 \frac{(x)(x-1)}{(2)(1)} | P(x) = 4 \frac{(x-1)(x-2)}{(-1)(-2)} + 3 \frac{(x)(x-2)}{(1)(-1)} + 6 \frac{(x)(x-1)}{(2)(1)} | ||
| \end{equation*} | \end{equation*} | ||
| + | |||
| + | This is mathematically clunky because it expresses a quadratic polynomial $P(x)$ as the sum of three quadratics, and we have a lot of tedious algebra to do to simplify. If we do that, we get | ||
| + | |||
| + | \begin{equation*} | ||
| + | P(x) = 4 - 3x + 2x^2 | ||
| + | \end{equation*} | ||
| + | |||
| + | which can be easily verified as passing through the given data points. | ||
| + | |||
| + | Further reading | ||
| + | * [[http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html | Lagrange Interpolating Polynomial]] (Wolfram Mathworld) | ||
| + | * [[https://en.wikipedia.org/wiki/Lagrange_polynomial| Lagrange Polynomial]] (Wikipedia) | ||
gibson/teaching/fall-2016/math753/lagrangepoly.1478896490.txt.gz ยท Last modified: 2016/11/11 12:34 by gibson
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