Question

1. Monomial least-squares (15 pts) Code. In code, determine the least-squares estimation of a monomial of degree $d$ using the $n$ data $[x_k, y_k]$ provided by the function $y = \sin x \cdot e^{-x^2}$ and computed with constant step in $x$ from $-1$ and $+1$. Plot and print out the points and fitting function for the following $(n, d)$ pairs: $(5,3)$, $(10,3)$, $(10,5)$. (This means you need to run your code with $n = 5$ and $d = 3$ and plot it, then run it again for $n = 10$ and $d = 3$ and plot that, etc.). Provide the results in the hard copy. 2. Harmonic least-squares (15 pts) Code. In code, using the same data $[x_k, y_k]$ created in Problem #1, continue the script code to perform a least-squares estimation using the harmonic function $y = a_0 + a_1 x + A \sin(2x + \varphi)$. That is: compute the unknown variables $[a_0, a_1, A, \varphi]$. Please plot and print out the points and fitting function for $n = 10$ and $n = 15$. Also report the values of the variables $[a_0, a_1, A, \varphi]$. Provide the results in the hard copy.

          1. Monomial least-squares (15 pts) Code. In code, determine the least-squares estimation of a monomial of degree $d$ using the $n$ data $[x_k, y_k]$ provided by the function $y = \sin x \cdot e^{-x^2}$ and computed with constant step in $x$ from $-1$ and $+1$. Plot and print out the points and fitting function for the following $(n, d)$ pairs: $(5,3)$, $(10,3)$, $(10,5)$. (This means you need to run your code with $n = 5$ and $d = 3$ and plot it, then run it again for $n = 10$ and $d = 3$ and plot that, etc.). Provide the results in the hard copy.
2. Harmonic least-squares (15 pts) Code. In code, using the same data $[x_k, y_k]$ created in Problem #1, continue the script code to perform a least-squares estimation using the harmonic function $y = a_0 + a_1 x + A \sin(2x + \varphi)$. That is: compute the unknown variables $[a_0, a_1, A, \varphi]$. Please plot and print out the points and fitting function for $n = 10$ and $n = 15$. Also report the values of the variables $[a_0, a_1, A, \varphi]$. Provide the results in the hard copy.

1. Monomial least-squares (15 pts) Code. In code, determine the least-squares estimation of a monomial of degree d using the n data [xk, yk] provided by the function y = sin x · e^-x^2 and computed with constant step in x from -1 and +1. Plot and print out the points and fitting function for the following (n, d) pairs: (5,3), (10,3), (10,5). (This means you need to run your code with n = 5 and d = 3 and plot it, then run it again for n = 10 and d = 3 and plot that, etc.). Provide the results in the hard copy.
2. Harmonic least-squares (15 pts) Code. In code, using the same data [xk, yk] created in Problem #1, continue the script code to perform a least-squares estimation using the harmonic function y = a0 + a1 x + A sin(2x + φ). That is: compute the unknown variables [a0, a1, A, φ]. Please plot and print out the points and fitting function for n = 10 and n = 15. Also report the values of the variables [a0, a1, A, φ]. Provide the results in the hard copy.

Added by Patricia G.

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