Numerical Analysis Assignment 5 — Curve Fitting and Interpolation
 Question #1
Consider the following set of data points:
 $x$ $y$ 0.1 0.03 0.3 0.06 0.8 0.07 1.1 0.1
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:
 $x$ $y$ 0.1 0.2 0.3 0.7 0.7 0.6
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. (c) A Newton polynomial.
 08.29.17
 $\pi$