Rate Of Convergence Of Newton_Raphson Method
Rate Of Convergence Of Newton_Raphson Method : Definition Of Rate Of Convergence : Rate of convergence is the speed of a convergent sequence to approach its limit point. General equation for rate of convergence is |εₙ₊₁|≤ c |εₙ|ᵖ where c is a constant , p= degree of rate of convergence Using this definition rate of convergence of Newton_ Raphson method can be calculated . Calculation Of Rate Of Convergence Of Newton_Raphson Method : The Newton_Raphson method in equation xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ) .......(1) Let ξ be the exact root of f(x) = 0 ( i.e f(ξ) = 0) Let xₙ,xₙ₊₁ be the approximate value at nth and (n+1)th iteration respectively . Similarly εₙ,εₙ₊₁ be the error at nth and (n+1)th iteration respectively . εₙ + ξ = xₙ εₙ₊₁ + ξ = xₙ₊₁ Substituting εₙ ,