As multiplication of polynomials in Matlab®, division of high degree of polynomials with low degree polynomials is also very easy. And you can see the division result as division result and remainder. In this article, we explained the division of polynomials with the ‘deconv()’ command in Matlab® with a very basic example below.
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>> numerator = [4 6 5 8 9 6 2 6 3];
denominator = [3 5 0 3 5];
[result, residual] = deconv(numerator, denominator)
result =
1.3333 -0.2222 2.0370 -2.0617 4.4362
residual =
Columns 1 through 5
0 0 0 0 0
Columns 6 through 9
-21.1811 -2.0000 3.0000 -19.1811
>> As you know, the division of high-degree polynomials with low-degree polynomials is a very tough process in calculus by hand. But in Matlab®, it is a very easy process. To divide high-degree polynomials with low-degree polynomials in Matlab®, you need to understand the logic of the definition of polynomials in Matlab®.
You can define your polynomial as vectors in Matlab®. We defined the high degree numerator polynomial and low degree enumerator polynomials vectors as shown in Matlab®. For example, ‘numerator’ named vector stands for the polynomial of 4x^8+6x^7+5x^6+8x^5+9x^4+6x^3+2x^2+6x+3. So you understand that each element of the polynomial vector in Matlab® represents the coefficient starting from the highest degree left to right.
As you know from calculus, the division of polynomials has a result and remainder. To see these results and remainder from this division example, we defined them as vector variables at the same time as shown above. Two variables called ‘result’ and ‘residual’ are defined for the deconv() command. You can use other kinds of names for variables.
Then numerator and denominator variables are typed in the parentheses of ‘deconv()’ in Matlab® as shown above. As you see again above, the result and residual is given as vectors with the same logic of ‘numerator’ and ‘denominator’.
The use of the ‘deconv()’ command to divide polynomials in Matlab® is very easy like above. Do not forget to leave your comments and questions about ‘deconv()’ command in Matlab® below!
This article is prepared for completely educative and informative purposes. Images used courtesy of Matlab®
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