Gauss Interpolation Formula
Gauss Interpolation Formula : The general Newton formula or Newton's Divided Difference Interpolation Formula gives y = f(x) = f(x₀)+(x-x₀)f(x₀,x₁)+(x-x₀) (x-x₁)f(x₀,x₁,x₂)+(x-x₀)(x-x₁) (x-x₂)f(x₀,x₁,x₂,x₃)+(x-x₀)(x-x₁)(x-x₂) (x-x₃)f(x₀,x₁,x₂,x₃,x₄)+(x-x₀)(x-x₁)(x-x₂)(x-x₃)(x-x₄)f(x₀,x₁,x₂,x₃,x₄,x₅)+(x-x₀)(x-x₁) (x-x₂)(x-x₃)(x-x₄) ×(x-x₅)f(x₀,x₁,x₂,x₃,x₄,x₅,x₆)+.... Now putting x₀=x₀ , x₁= x₀+h ,x₂= x₀-h, x₃= x₀+2h ,x₄=x₀-2h ,x₅=x₀+3h ,x₆=x₀-3h We immediately get f(x) = f(x₀)+(x-x₀)f(x₀,x₀+h)+(x-x₀)(x-x₀-h) f(x₀,x₀+h,x₀-h)+(x-x₀)(x-x₀-h)(x-x₀+h) f(x₀,x₀+h,x₀-h,x₀+2h)+(x-x₀)(x-x₀-h) (x-x₀+2h)f(x₀,x₀+h,x₀-h,x₀+2h,x₀-2h) + (x-x₀)(x-x₀-h)(x-x₀+h)(x-x₀-h)(x-x₀+2h) f(x₀,x₀+h,x₀-h,x₀+2h,x₀-2h,x₀+3h)+.... .....