Numerical Analysis Assignment #5 — Curve Fitting and Interpolation  
Question #1
Consider the following set of data points:
$x$$y$
0.10.03
0.30.06
0.80.07
1.10.1
Fit the curve $y=C_1+C_2 \sqrt{x}+C_3 x$ through the latter data with $C_1$, $C_2$, and $C_3$ some constants determined through the method of least squares.
09.26.16
Question #2
Consider the following set of data points:
$x$$y$
0.10.2
0.30.7
0.70.6
Find an expression $y(x)$ that fits through every data point using
(a)  a Vandermonde polynomial
(b)  a Lagrange polynomial
(c)  a Newton polynomial
Question #3
You obtain a polynomial of degree 3 that yields $y$ as a function of $x$ from 4 data points ($x_1,y_1$), ($x_2,y_2$), ($x_3,y_3$), ($x_4,y_4$). Knowing the polynomial coefficients, determine the minimum number of arithmetic operations (additions, subtractions, multiplications, and divisions) necessary to calculate $y$ as a function of $x$ from $x=0$ to $x=1$ using a step $\Delta x=0.01$ for
(a)  A Vandermonde polynomial.
(b)  A Lagrange polynomial.
(b)  A Newton polynomial.
08.29.17
Answers
1.  
2.  
3.  808, 2751, 1111.
Due on November 22nd at 16:30. Do Questions #1, #2, and #3.
11.15.17
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