How to determine where the function is equal to zero

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Lauren Stearns
Lauren Stearns 2017-5-10
评论： Lauren Stearns 2017-5-11
Ultimately I need to figure out the first time my function is equal to zero, but to start I just want to save the x value as a new variable whenever y = 0. Here is my code so far:
close all; clear all; clc
% Prepared by Lauren Stearns
x= 0:10;
x(1)= 1E-5;
f= @(x) (2*besselj(1,x)./x).^2; % The Given Function
y=f(x) % replace the first element in the array
plot(x,y,'b-'); % Plot the Airy pattern
hold on;
xq=0:10; % Points of inquiry
xq(1)=0.0001;
yq3 = interp1(x,y,xq,'cubic'); % Cubic Interpolation
plot(xq,yq3,'b.'); % Plotting the Cubic Interpolation
for y = 0 % Trying to save the x value as a new variable
when y = 0
x = Dark_Fringe
end
xlabel('x');
ylabel('f(x)');
title('Airy Pattern Three');
disp(Dark_Fringe)

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采纳的回答

Matt J
Matt J 2017-5-10
编辑：Matt J 2017-5-10
Ultimately I need to figure out the first time my function is equal to zero,
This is the simpler of the two problems. It is equivalent to finding where the bessel function is equal to zero. Using online tables or your plots, you can see that the first root lies in the interval [3.5,4.5]
>> [xroot,fval] = fzero(@(x) besselj(1,x), [3.5,4.5])
xroot =
3.8317
fval =
7.2971e-17
You can do similarly for the other roots in the interval [0,10]

更多回答（1 个）

Ahmed Hossam
Ahmed Hossam 2017-5-10
Try to use symbolic calculation to find 'the zeros'. Otherwise use numerical newton raphson algorithm.

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