Bilinear interpolation
= Bilinear interpolation
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On a rectangle, <bilinear interpolation> is linear in each coordinate separately and matches the four corner values. With normalized coordinates $s,t\in[0,1]$, it is $(1-s)(1-t)u_{00}+s(1-t)u_{10}+(1-s)tu_{01}+stu_{11}$. A <multigrid method> can use it to prolong a coarse correction to finer-grid nodes. It is not generally an affine function of the pair $(s,t)$, since it can contain a mixed $st$ term.