Page 20 - Numerical Analysis Using MATLAB and Excel

Evaluation of a Polynomial at Specified Values

7
9
8
p Þ p = 2x 11 – 6x 10 – 8x + 34x + 18x – 24x 6
1
2
5 4 3 2
– 74x 88x +– 78x + 166x + 174x + 108
We can write MATLAB statements in one line if we separate them by commas or semicolons.
Commas will display the results whereas semicolons will suppress the display.

Example 1.7

Let
7
3
5
p = x – 3x + 5x + 7x + 9 (1.6)
3
6
2
5
p = 2x – 8x + 4x + 10x + 12
4
Compute the quotient p p 4 using the deconv(p,q) function.
⁄
3
Solution:
p3=[1 0 −3 0 5 7 9]; p4=[2 −8 0 0 4 10 12]; [q,r]=deconv(p3,p4)
q =
0.5000
r =
0 4 -3 0 3 2 3
Therefore, the quotient qx() and remainder rx() are

5
4
2
qx() = 0.5 r x() = 4x – 3x + 3x + 2x + 3

Example 1.8
Let
2
4
6
p = 2x – 8x + 4x + 10x + 12 (1.7)
5
Compute the derivative dp dx⁄ using the polyder(p) function.
5
Solution:

p5=[2 0 −8 0 4 10 12];
der_p5=polyder(p5)
der_p5 =
12 0 -32 0 8 10
Therefore,

Numerical Analysis Using MATLAB® and Excel®, Third Edition 1−7
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