In the following lecture:


the model (formula) for solving the linear interpolation problem (1D) given at p.5 is:

$f(x)= a_1x_1 + a_0x_0$

solve for $a1,a0$

the system:

$f(0)=a_i*0 + a_0*1$


$f(1)=a_i*1 + a_0*1$

I don't understand where this formula comes from. Even though deriving in all possible ways I could think of, I cannot get the equation of a line $y=mx+b$ ( also written as: $f(x)= mx+b$, where m is the slope and b is the y-intercept) to look something like $f(x)= a_1x_1 + a_0x_0$. Any idea/proposals/discussions etc.?


To my eye, the equations in the slides look like $f(x) = a_1 x^1 + a_0 x^0 = a_1 x + a_0$. So it's an exponent on the $x$, not an index. As long as you are interpolating linear, the only exponents that you encouter are 1 (linear) and 0 (constant). When you go to quadratic, you'll see $x^2$ terms appearing. Now, $a_1$ is the coefficient of the linear term (your slope $m$) and $a_0$ is the coefficient of the constant term (the y-intercept $b$).

This should explain where the system of equations for $a_1$ and $a_0$ comes from.

  • $\begingroup$ yes thanks, I should have thought about that... its clearly and exponent as you say,. so the x^0 = 1. must have been tired... I was doing nonsense $\endgroup$ – Machupicchu Aug 19 '19 at 12:32
  • $\begingroup$ They want to find the coefficients slope a1 and intercept a0 that work for both points x=0 and x=1 $\endgroup$ – Machupicchu Aug 19 '19 at 12:41

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