Bernstein polynomial approximating a function
bernstein(n, f, x)
function (specified as a procedure or operator)
This procedure returns the nth degree Bernstein polynomial in x approximating the function f(x) on the interval 0,1. Note that f must be a function of one variable specified as a procedure or operator.
Bernstein polynomials arise in the Stone-Weierstrass approximation theorem of analysis that says any continuous function (R->R) can be uniformly approximated on a closed interval by a sequence of polynomials. The Bernstein polynomials are one such set for doing this.
Given p≔n,i,x↦ni⁢xi⁢1−xn−i Bernstein is defined to be
f := proc(t) if t < 1/2 then 4*t^2 else 2 - 4*t^2 end if end proc:
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