Numerical Analysis
Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 10.3, Problem 1E

a.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

a.

Expert Solution
Check Mark

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 1 andcos2πt

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 1 andcos2πt

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 

  P4(t)=0+0cos2πt+sin2πt+0cos2πt .

Therefore, the approximating function is  P2(t)=0 .

b.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

b.

Expert Solution
Check Mark

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 1 andcos2πt

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 1 andcos2πt

.Similar to (a).

Dropping all but the first two terms from the trigonometric interpolating function

  P4(t)=cos2πt+sin2πt  yields  P2(t)=cos2πt .

c.

To determine

To find: the best order 2 least squares approximation to the data using the basic function 1 andcos2πt

c.

Expert Solution
Check Mark

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 1 andcos2πt

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 1 andcos2πt

Similar to (a). Dropping all but the first two terms from the trigonometric interpolating function

  P4(t)=cos4πt yields  P2(t)=0 .

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