Polynomial division - derived form covolution

Polynomial division is derived directly from convolution matrix.

Description

For the division of univariate polynomials, given the dividend b(x) of degree n and the divisor a(x) of degree m, such that b(x)/a(x) = q(x) + r(x)/a(x), the quotient q(x) of degree n-m and the remainder r(x) of degree m-1 are then obtained.

Coefficients of the desired q_k and r_k from the given b_k and a_k are directed determined by the convolutional approach.

This process is much faster then familier long polynomial division and synthetic plynomial division.

This short and fast code is similar to the MATLAB built-in function 'deconv.m'.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Polynomial division by convolution - quotient and reminder, Polynomial division by convolution -- up to finite terms

• MATLAB release: MATLAB 6.5 (R13)