Horner's Rule

• evaluate p(x) = a_nxⁿ + a_n-1x^n-1 + ... + a₁x¹+a₀
• Brute Force

  • BRUTE_POLY_EVAL(A,x)
    
     sum ← 0
     for i ← 0 to n do
        sum ← sum + A[i]*pow(x,i)
     return sum
    
    	

  • The standard questions.
• Horner's Method (or Rule)
  • Note, there are two things named Horner's Method.
    • This one.
    • A root approximation method.
  • This algorithm is old (see Qin Jiushao)

  • HORNER(A,x)
    
     sum ← A[n]
     for i ← n-1 downto 
        sum ← x * sum + A[i]
     return sum
    
    	

  • The standard questions.