Questions tagged [interpolation]

Questions on interpolation, the estimation of the value of a function from given input, based on the values of the function at known points. It is necessary because in science and engineering we often need to deal with discrete experimental data.

1,435 questions
Filter by
Sorted by
Tagged with
25 views

Error estimation of the Taylor polynomial

Suppose that the signal $x: \mathbb{R} \rightarrow \mathbb{R}$ and its first $m$ derivatives are sampled at time $t_k$ and $t_{k+1}$ and there, i.e. the following values are available: \begin{aligned} ...
51 views

How might I define a parabola in vertex form, such that…

Given the formula for a parabola in vertex form: $y = a(x-h)^2+k$, as $h$ and $k$ are changed, the $a$ value will adjust in order to keep the left hand $x$-intercept anchored to the origin. I'm really ...
22 views

10k views

Spatial Interpolation for Irregular Grid

How would I interpolate to a point P if I have four points around it such that: Q1 = (x1,y1), Q2 = (x2,y2), Q3 = (x3,y3), Q4 = (x4,y4) If the coordinates formed a regular 2D grid I would use a ...
45 views

Weighted moving average derived from parabola approximation

Let us have five points at $x = -2,-1,0,1,2$ with ordinates equal to $y_i$, I want to derive the formula for $a_0$, such that the parabola $y = a_0 + a_1x + a_2x^2$ fits the points the best in ...
41 views

Continuous function for day/night with night being c times longer than day

I'm looking for a function to transform domain $[0,1)$ into range $[0,1)$ such that the size of the domain corresponding to the range interval $[.5,1)$ is $c$ times the size of the domain ...
17 views

Error norm for finite difference approximation

I have approximated the differential equation using finite difference approximation and have the vector $u$. To find the error norm, it says I need the exact solution and the piecewise linear ...
8 views