diary('sept11_diary.txt')
phi = @(x) x/2 - 1/x

phi =

  <a href="matlab:helpPopup function_handle" style="font-weight:bold">function_handle</a> with value:

    @(x)x/2-1/x

x=1

x =

     1

x = phi(x)

x =

  -0.500000000000000

phi = @(x) x/2 _ 1/x
 phi = @(x) x/2 _ 1/x
                ↑
{Error: Invalid text character. Check for unsupported symbol, invisible character, or pasting
of non-ASCII characters.
} 
phi = @(x) x/2 + 1/x

phi =

  <a href="matlab:helpPopup function_handle" style="font-weight:bold">function_handle</a> with value:

    @(x)x/2+1/x

x = phi(x)

x =

  -2.250000000000000

x=1

x =

     1

x = phi(x)

x =

   1.500000000000000

x = phi(x)

x =

   1.416666666666667

x = phi(x)

x =

   1.414215686274510

sqrt(2)

ans =

   1.414213562373095

x = phi(x)

x =

   1.414213562374690

x = phi(x)

x =

   1.414213562373095

sqrt(2)

ans =

   1.414213562373095

x=1

x =

     1

x=phi(x); abs(sqrt(2)-x)

ans =

   0.085786437626905

x=phi(x); abs(sqrt(2)-x)

ans =

   0.002453104293571

x=phi(x); abs(sqrt(2)-x)

ans =

     2.123901414519125e-06

x=phi(x); abs(sqrt(2)-x)

ans =

     1.594724352571575e-12

x=phi(x); abs(sqrt(2)-x)

ans =

     2.220446049250313e-16

x=phi(x); abs(sqrt(2)-x)

ans =

     2.220446049250313e-16

x=phi(x); abs(sqrt(2)-x)

ans =

     2.220446049250313e-16

x=1

x =

     1

for k=1:5
end
root = []

root =

     []

for k=1:5
x=phi(x)
root(k)=x
end

x =

   1.500000000000000


root =

   1.500000000000000


x =

   1.416666666666667


root =

   1.500000000000000   1.416666666666667


x =

   1.414215686274510


root =

   1.500000000000000   1.416666666666667   1.414215686274510


x =

   1.414213562374690


root =

   1.500000000000000   1.416666666666667   1.414215686274510   1.414213562374690


x =

   1.414213562373095


root =

  Columns 1 through 4

   1.500000000000000   1.416666666666667   1.414215686274510   1.414213562374690

  Column 5

   1.414213562373095

root

root =

  Columns 1 through 4

   1.500000000000000   1.416666666666667   1.414215686274510   1.414213562374690

  Column 5

   1.414213562373095

err = sqrt(2)-root

err =

  Columns 1 through 4

  -0.085786437626905  -0.002453104293571  -0.000002123901415  -0.000000000001595

  Column 5

   0.000000000000000

err(2)/err(1)^2

ans =

  -0.333333333333301

err(3)/err(2)^2

ans =

  -0.352941176431442

err(4)/err(3)^2

ans =

  -0.353522384561164

err(5)/err(4)^2

ans =

     8.731100212881161e+07

phi = @(x) x - (1+x)^2*atan(x)

phi =

  <a href="matlab:helpPopup function_handle" style="font-weight:bold">function_handle</a> with value:

    @(x)x-(1+x)^2*atan(x)

atan(0)

ans =

     0

x=2

x =

     2

x=phi(2)

x =

  -7.964338460146813

x=phi(x)

x =

  62.164246367259913

x=phi(x)

x =

    -6.140701648634737e+03

x=phi(x)

x =

     5.920035892552534e+07

x=phi(x)

x =

    -5.505142460312904e+15

x=phi(x)

x =

     4.760548576056652e+31

x=phi(x)

x =

    -3.559867872264201e+63

x=phi(x)

x =

    1.990616662886448e+127

x=phi(x)

x =

   -6.224366365223755e+254

x=phi(x)

x =

   Inf

x=phi(1)

x =

  -2.141592653589793

x=phi(x)

x =

  -0.663799920119523

x=phi(x)

x =

  -0.597562320753766

x=phi(x)

x =

  -0.510328697987646

x=phi(x)

x =

  -0.397183129957967

x=phi(x)

x =

  -0.259794895466705

x=phi(x)

x =

  -0.120530988349953

x=phi(x)

x =

  -0.027751959730115

x=phi(x)

x =

  -0.001525700297281

phi

phi =

  <a href="matlab:helpPopup function_handle" style="font-weight:bold">function_handle</a> with value:

    @(x)x-(1+x)^2*atan(x)

phi = @(x) x - (1+x^2)*atan(x)

phi =

  <a href="matlab:helpPopup function_handle" style="font-weight:bold">function_handle</a> with value:

    @(x)x-(1+x^2)*atan(x)

x=phi(1)

x =

  -0.570796326794897

x=phi(x)

x =

   0.116859903998913

x=phi(x)

x =

  -0.001061022117045

x=phi(x)

x =

     7.963096044106416e-10

x=phi(x)

x =

     0

diary