Question

I am trying to multiply two polynomials A & B each of degree ‘d’, in this there are basically two operations i.e. Multiply & Addition. In order to get an output polynomial ‘C’, how many total number of operations required?
I have searched a lot and I make assumption that total multiplication operations will be ‘d^2’ & total additions will be ‘2d-1’. Therefore total operations will be (2d-1)*(d^2).
is this true? or false? and how?
Please suggest….

Answer 1

A polynomial of degree d has d+1 coefficients. So a simple implementation would require (d+1)^2 multiplications. For very large d the number of operations can be reduced to O( d log(d)) using FFT.