Concept

Combing approximation function with different step to reduce the most significant error item.

Example

̃𝐹() is approximation to 𝐹 where ̃𝐹()=𝐹+𝑐17+𝑂(9) and we want to reduce the 7 error term.
We can use ̂𝐹()=𝛼̃𝐹()+𝛽̃𝐹(2) as new approximation where

  • 𝛼+𝛽=1 hold, because we need at least ̂𝐹()𝐹 hold to keep accuracy, other wise it will has term with (1+𝜀)𝐹
  • 𝑐1(𝛼7+𝛽(2)7)=0 to reduce the term