Reconfigurable Hardware Implementation of a Multivariate Polynomial Interpolation Algorithm

Algorithm 1

Algorithm to determine the collection of bases.

for  𝑖∶=0 to 𝑏−1  do

    𝑅=1;

    for  𝑗∶=0 to 𝑏−1,𝑗≠𝑖  do

        𝑟(𝑖,𝑗)=⋁_{(𝑢,𝑣)∈𝑆𝑓,𝑖×𝑆𝑓,𝑗}{𝑥_𝑘|𝑢_𝑘≠𝑣_𝑘}

    end

    𝑅=𝑅∧𝑟(𝑖,𝑗);

    Express 𝑅 in disjunctive normal form (DNF)

end