I had the curve of a function,(eg $A\sin(x)+Bx+C=f(x)$) and i wanted to know A,B and C , so i took 3 points on the curve and solved $3$ equations and $3$ unknowns linearly.
The problem was when i took 3 points close to each other (eg $x=0.001 , 0.001008, 0.001009$) the answers would have a huge error. i searched about this problem online, some pages suggested it was an error in the approximate matrix inversion but i guess they were wrong because i tried gaussian elimination and it didn't work either.
Another page suggested it's an error because of error in float numbers arithmetic but my friend (studying computer science) says it shouldn't make that much error in the final answers So i wanted to know if this problem is a mathematical problem or a computational one? for example consider the following points, the first set yields false answers and the second one yield correct ones ( first column is x , second is f(x) and third is answers if we solved it with these points) points.
The error might not seem large in this case , but as the function grows more complex and the unknows increase, the error will increase