## Polynomial division by convolution - quotient and reminder

Version 1.34.0.0 (1.58 KB) by
Division of two polynomials to get quotient and reminder using convolution matrix.

Updated Thu, 07 Jul 2011 09:20:26 +0000

Polynomial division by convolution matrix approach.

Given b(x) and a(x), and find q(x) and r(x) in
b(x) = a(x)*q(x) + r(x)
where
b(x) = b(0)+ ... +b(k)*x^k + ... +b(n)*x^n
a(x) = a(0)+ ... +a(k)*x^k + ... +a(m)*x^m
q(x) = q(0)+ ...+ q(k)*x^k + ... +q(n-m)*x^(n-m)
r(x) = r(0)+ ...+ r(k)*x^k + ... +r(m-1)*x^(m-1)

If coefficients of b(x) and a(x) are all integers, then the entire process may involve mostly integer arithmetric operations. The roundoff errors may thus be eliminated.

This code is similar to the MATLAB's built-in function: 'deconv.m'.

### Cite As

Feng Cheng Chang (2023). Polynomial division by convolution - quotient and reminder (https://www.mathworks.com/matlabcentral/fileexchange/19565-polynomial-division-by-convolution-quotient-and-reminder), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R13
Compatible with any release
##### Platform Compatibility
Windows macOS Linux
##### Acknowledgements

Inspired by: Calculates inverse Z-transform by long division

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Version Published Release Notes
1.34.0.0

update the m file

1.33.0.0

Update the m-file, to include any polynomials with both leading and trailing zero coefficients.

1.32.0.0

Correct typo in Description, and update the M-file.

1.0.0.0