Concept explainers
a.
To find: the best order 2 least squares approximation to the data using the basic function
a.
Explanation of Solution
Given information:
The initial conditions that are given are,
here is the best order 2 least squares approximation to the data using the basic function
Calculation:
As it’s known that by using DFT equation here is the best order 2 least squares approximation to the data using the basic function
According to Theorem 10.11, the order 2 least square approximation results from dropping all but the first two terms in the trigonometric interpolating function
Therefore, the approximating function is
b.
To find: the best order 2 least squares approximation to the data using the basic function
b.
Explanation of Solution
Given information:
The initial conditions that are given are,
here is the best order 2 least squares approximation to the data using the basic function
Calculation:
As it’s known that by using DFT equation, here is the best order 2 least squares approximation to the data using the basic function
.Similar to (a).
Dropping all but the first two terms from the trigonometric interpolating function
c.
To find: the best order 2 least squares approximation to the data using the basic function
c.
Explanation of Solution
Given information:
The initial conditions that are given are, here is the best order 2 least squares approximation to the data using the basic function
Calculation:
As it’s known that by using DFT equation, here is the best order 2 least squares approximation to the data using the basic function
Similar to (a). Dropping all but the first two terms from the trigonometric interpolating function
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Chapter 10 Solutions
Numerical Analysis
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