bernstein - Maple Help
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bernstein

Bernstein polynomial approximating a function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

bernstein(n, f, x)

Parameters

n

-

integer

f

-

function (specified as a procedure or operator)

x

-

algebraic expression

Description

• 

This procedure returns the nth degree Bernstein polynomial in x approximating the function f(x) on the interval .  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  Bernstein is defined to be

Examples

(1)

f := proc(t) if t < 1/2 then 4*t^2 else 2 - 4*t^2 end if end proc:

(2)

See Also

binomial

polynomials

 


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