Linear interpolation
= Linear interpolation
{title2=$(1-t)f(a)+tf(b)$}
{wiki}
Between two prescribed values, <linear interpolation> assigns $(1-t)f(a)+tf(b)$ at $(1-t)a+tb$, for $0\leq t\leq1$. Joining successive samples produces a <piecewise-linear function>. For a <continuous function> on a compact interval, interpolants along grids with mesh tending to zero converge in the <uniform norm>; their error is bounded by the <modulus of continuity> at the mesh size.