How do I iterate f(x)

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.

[Torsten]

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]

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.

Answer 1

[Alan Weiss]

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]'

Number of iterations is not too high.

Alan Weiss

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