How do I iterate f(x)

Question

LILIA VERGARA 2023-1-26

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1901525-how-do-i-iterate-f-x

回答： Alan Weiss 2023-1-27

在 MATLAB Online 中打开

using x^(0) = 0 and x^(1) = 5 as inital condition

I am trying to iterate f(x) up to 60 iterations or till the estimated relative error is less than 10^-6

note that f(x) = e^x - 2 - x - (x^2 / 2)

The code I have startead with has been giving me errors:

f = @(x)exp(x) - 2 - x - x.^2./2
f = function_handle with value:
    @(x)exp(x)-2-x-x.^2./2
x_true = fzero(f,[0.01 0.1],optimset("Display","iter"));
 
Error using fzero
Function values at the interval endpoints must differ in sign.

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Torsten 2023-1-26

What do you mean by

I am trying to iterate f(x) up to 60 iterations or till the estimated relative error is less than 10^-6

?

Walter Roberson 2023-1-26

在 MATLAB Online 中打开

f = @(x)exp(x) - 2 - x - x.^2./2

f = function_handle with value:

@(x)exp(x)-2-x-x.^2./2

fplot(f, [0.01 0.1])

There is no zero of the function within that range.

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Answer 1

Alan Weiss 2023-1-27

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1901525-how-do-i-iterate-f-x#answer_1157725

在 MATLAB Online 中打开

Is this what you are looking for?

f = @(x)exp(x) - 2 - x - x.^2./2;

t = linspace(0,5);

plot(t,f(t))

OK, there is a root in that interval. Find it.

[x,fval,eflag,output] = fzero(f,[0 5])
x = 1.5681
fval = 2.2204e-16
eflag = 1
output = struct with fields:
    intervaliterations: 0
            iterations: 11
             funcCount: 13
             algorithm: 'bisection, interpolation'
               message: 'Zero found in the interval [0, 5]'