Construct Lagrange interpolating polynomials of degree two and three to approximate: a)$ f (0.25)$ yes $f(0.1) = -0.62049958, f(0.2) = -0.28398668, f(0.3) = 0.00660095, f(0.4) = 0.24842440 $
Additionally, you must calculate the error rate for each case.
Guys, I have done this exercise and obtained the following: For the polynomial of degree two
$-2.438209x^2+4.1249808x-1.01145448$
when approaching $0.25$
$-2.438209(0.25)^2+4.1249808(0.25)-1.01145448= -0.1325973425$
And for grade three:
$-0.4731516667x^3-2.0123725x^2+4.001961367x-1.00009884$
By approximating I obtained the following: $-0.4731516667(0.25)^3-2.0123725(0.25)^2+4.001961367(0.25)-1.00009884= -0.1327747743$
They ask me to calculate the error rate for both grade 2 and 3, my question is: how do I apply the error rate? According to Lagrange's formula, the derivative of the function must be calculated, but what would the function be in this case? I found Burden's book pág 115-119 regarding the error calculation but I can't understand the notation. I hope you can help me.