Can someone help me to draw a function having the Bolzano-Weierstrass property?

5 次查看（过去 30 天）
Munteanu Alexandru
Munteanu Alexandru 2011-6-26
Hello
I have a project about continuous function. And I have to write a code in Matlab that draws the a function with Bolzano-Weierstrass property?
Can someone explain me how to do it? Or a little piece of code that can help me?
Thank you very much, Alex
PS Sorry for my bad English.
  2 个评论
Andrew Newell
Andrew Newell 2011-6-27
Can a single function have the BZ property? I thought it applied to sets of points or functions.
Munteanu Alexandru
Munteanu Alexandru 2011-6-28
Bolzano’s theorem
If a function f(x) is continuous on a closed interval [a,b] and f(a) and f(b) are of different sign, there exists at least a point c between a and b such that f(c)=0.
i was thinking to make a function like myfucntion(thefunction,interval1,interval2) and inside to make a linspace from interval1 to interval2 and a polyval of thefunction and my intervals. after that to plot the result into something. but i don't know exactly how to do it.
thanks

请先登录，再进行评论。

请先登录，再回答此问题。

回答（2 个）

Matt Dunham
Matt Dunham 2011-7-2
function y = weierstrass(x, a, b, n)
%%The Weierstrass function
% This is an example of a function which is everywhere continuous, but
% nowhere differentiable.
%
%
%%INPUTS
% x - a scalar or vector
% b - [7] an odd integer
% a - [0.82] a double between 0 and 1
%
% such that a*b > 1 + 1.5*pi
%
% n - [~300] summation limit, (in the true function this is inf) but here
% you must
% pick a finite value for the approximation. If you pick too large a
% value, you'll get NANs since b^n can easily exceed realmax. By
% default, the largest possible n is chosen.
%
% See http://en.wikipedia.org/wiki/Weierstrass_function
%
%%OUTPUT
% y - same dimensions as x, (the output of the function)
%
If no inputs are given, this line is called: plot(-2:0.005:2, weierstrass(-2:0.005:2, 0.82, 7, 363));
%%Matt Dunham (July 2, 2011)
if nargin < 2, a = 0.82; end
if nargin < 3, b = 7; end
if nargin < 4, n = floor(log(realmax)/log(b)) - 1; end
if nargin < 1
plot(-2:0.002:2, weierstrass(-2:0.002:2));
return
end
assert(mod(b, 2) > 0); % b must be odd
assert(a > 0 && a < 1);
assert((a*b) > (1 + 1.5*pi));
y = sum(bsxfun(@times, a.^(0:n), cos(pi*bsxfun(@times, b.^(0:n), x(:)))), 2);
end
Floris
Floris 2011-6-29
If it can be any function you have to plot, just make a linear one?
say: x1 = a, y1 = f(a), x2 = b, y2 = f(b), with (as given) f(a) and f(b) a different sign. Then just make the line y=M*x+C through the points (x1,y1) and (x2,y2). There is going to be a point c for which f(c)=0. It can even be easily found analytically.
Or do I misunderstand your problem?
  1 个评论
Munteanu Alexandru
Munteanu Alexandru 2011-7-3
I had to do for all possible functions. And I hat to find first if the intervals had different sings and the function is continuous. And plot the functions between those intervals, and on the results to show in how many points (f(c)) equals 0.

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Matrix Indexing 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by