Good Evening,
Context:
I wanted to count the operations for calculate the coefficents in the newton base if you have $n+1$ datas.
$$f_j=p_j(x_j)=a_0+\sum_{i=1}^j(a_i\prod_{k=0}^{{i-1}}(x_j-x_k))\ \ \ j,i=1,..,n$$
maybe you can help me to understand the counting in my script, because I have another solution. I want to count how many operations I need to calculate this:
$$a_j=\frac{f_j-a_0-\sum_{i=1}^{j-1}(a_i\prod_{k=0}^{i-1}(x_j-x_k)}{\prod_{k=0}^{j-1}(x_j-x_k)}$$
I would say, we have in the deonominator $j$ subtractions and $j-1$ multiplications. In the numerator we have $1+2+...+(j-1)$ Subtractions and also $1+2+...+(j-1)$ multiplications and then $j$ subtractions and in the end one Divsion.
Thats what I found in my script, but does not the 1 subtraction $-a_0$ is missing?
Thanks for helping me!:)