The goal of this problem is to fit a trigonometric function of the form f(t) = co + c1 sin(t) to the data points (0, –9.5), (5, –11.5), (7, –9.5), (*,-1.5), using least squares. (a) The problem is equivalent to finding the least squares solution to the system Xc=y where X = y = and c = [c1, c2]" (b) Find the coefficients of the best fit by finding the least squares solution to the system in part (a) Co = Ci =
The goal of this problem is to fit a trigonometric function of the form f(t) = co + c1 sin(t) to the data points (0, –9.5), (5, –11.5), (7, –9.5), (*,-1.5), using least squares. (a) The problem is equivalent to finding the least squares solution to the system Xc=y where X = y = and c = [c1, c2]" (b) Find the coefficients of the best fit by finding the least squares solution to the system in part (a) Co = Ci =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![The goal of this problem is to fit a trigonometric function of the form \( f(t) = c_0 + c_1 \sin(t) \) to the data points \((0, -9.5), \left(\frac{\pi}{2}, -11.5\right), (\pi, -9.5), \left(\frac{3\pi}{2}, -1.5\right)\), using least squares.
(a) The problem is equivalent to finding the least squares solution to the system \(\mathbf{Xc} = \mathbf{y}\) where
\[
X = \begin{bmatrix}
& \\
& \\
& \\
&
\end{bmatrix}
, \quad y = \begin{bmatrix}
\\
\\
\\
\end{bmatrix}
\]
and \( c = [c_1, c_2]^T \)
(b) Find the coefficients of the best fit by finding the least squares solution to the system in part (a)
\[ c_0 = \]
\[ c_1 = \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70a05657-0307-4b7c-962c-ab3824846297%2Fd10cc169-411f-4a2f-a67b-a105ae05d40b%2F1gq5anj_processed.png&w=3840&q=75)
Transcribed Image Text:The goal of this problem is to fit a trigonometric function of the form \( f(t) = c_0 + c_1 \sin(t) \) to the data points \((0, -9.5), \left(\frac{\pi}{2}, -11.5\right), (\pi, -9.5), \left(\frac{3\pi}{2}, -1.5\right)\), using least squares.
(a) The problem is equivalent to finding the least squares solution to the system \(\mathbf{Xc} = \mathbf{y}\) where
\[
X = \begin{bmatrix}
& \\
& \\
& \\
&
\end{bmatrix}
, \quad y = \begin{bmatrix}
\\
\\
\\
\end{bmatrix}
\]
and \( c = [c_1, c_2]^T \)
(b) Find the coefficients of the best fit by finding the least squares solution to the system in part (a)
\[ c_0 = \]
\[ c_1 = \]
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