Curve fitting with derivatives

[markraz]

Hi I am trying to learn how to curve fit with derivatives. (I understand derivatives/power rule)
I found an example here: https://math.stackexchange.com/questions/1882772/curve-fitting-with-derivatives
it is illustrated as follows( I hope it's ok that I just cut and pasted):

template


data set


Ax=b


So my question is, how did they get the b vector? (y y' and y" values of the data set.) Where do the numbers 1251?? 1128? 1167 come from? I don't understand. also why do you think he put fractions in front of the vectors in the data set?
Any help would be appreciated
Thanks in advance

 

[HallsofIvy]

As far as "why did he put fractions in front of the vectors like that?", I presume that is how the data was given! Perhaps whoever compiled the data didn't like decimal fractions. As far as "where do the numbers 1251, 1128, and 1167 come from, they come from the given y vector where the first three values are 417, 376, and 389, each multiplied by 1/500. The fractions in front of the three "vectors" are 1/10, 1/500, and 1/6 which have a "least common denominator" of 1500.

417/500=417(3)/500(3)= 1251/1500, 376/500= 376(3)/500(3)= 1128/1500, and 398/500= 389(3)/500(3)= 1167/1500.

 

[Deleted member 4993]

Hi I am trying to learn how to curve fit with derivatives. (I understand derivatives/power rule)
I found an example here: https://math.stackexchange.com/questions/1882772/curve-fitting-with-derivatives
it is illustrated as follows( I hope it's ok that I just cut and pasted):

template
View attachment 21952

data set
View attachment 21953

Ax=b
View attachment 21954

So my question is, how did they get the b vector? (y y' and y" values of the data set.) Where do the numbers 1251?? 1128? 1167 come from? I don't understand. also why do you think he put fractions in front of the vectors in the data set?
Any help would be appreciated
Thanks in advance

y = $\displaystyle a_o + a_1*x + a_2*x^2 + a_3*x^3$

What would be y' , y" & y'"?

Now look at those numbers again!