Polynomial division by convolution - quotient and reminder

Division of two polynomials to get quotient and reminder using convolution matrix.


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

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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)
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
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Version Published Release Notes

update the m file

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

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