f = inline('3*cos(4*x) + 14*cos(2*x).*sin(x) - 15*cos(2*x) - 11*sin(x) + 11')

f =

     Inline function:
     f(x) = 3*cos(4*x) + 14*cos(2*x).*sin(x) - 15*cos(2*x) - 11*sin(x) + 11

g = inline('-12*sin(4*x) + 14*(-2*sin(2*x).*sin(x)+cos(2*x).*cos(x))+30*sin(2*x)-11*cos(x)')

g =

     Inline function:
     g(x) = -12*sin(4*x) + 14*(-2*sin(2*x).*sin(x)+cos(2*x).*cos(x))+30*sin(2*x)-11*cos(x)

newton(f, g, -0.5, 0.0000000001, 0.5)

r =

  -0.33983690945412


ans =

  |       x_i       |      g(x_i)      |       error      |   error ratio   |


ans =

  -0.50000000000000  -0.38499267963579   0.16016309054588                  0
  -0.38499267963579  -0.34519615006708   0.04515577018166   0.28193618159941
  -0.34519615006708  -0.33992694933625   0.00535924061296   0.11868340616054
  -0.33992694933625  -0.33983693552615   0.00009003988213   0.01680086576319
  -0.33983693552615  -0.33983690945412   0.00000002607203   0.00028956085939
  -0.33983690945412  -0.33983690945412   0.00000000000000   0.00000009368243
  -0.33983690945412  -0.33983690945412   0.00000000000000   0.11363636363636

newton(f, g, 0.5, 0.0000000001, 0.5)

r =

   0.52359630078870


ans =

  |       x_i       |      g(x_i)      |       error      |   error ratio   |

Warning: Divide by zero.
> In <a href="error:/afs/csl.tjhsst.edu/user/mlee1/num-a/fpi_err.m,10,1">fpi_err at 10</a>
  In <a href="error:/afs/csl.tjhsst.edu/user/mlee1/num-a/newton.m,13,1">newton at 13</a>

ans =

   0.50000000000000   0.50788132816905   0.02359630078870                  0
   0.50788132816905   0.51312651126278   0.01571497261964   0.66599306223336
   0.51312651126278   0.51661975397137   0.01046978952591   0.66623021110634
   0.51661975397137   0.51894714334656   0.00697654681733   0.66635024515628
   0.51894714334656   0.52049813681164   0.00464915744213   0.66639808545208
   0.52049813681164   0.52153187784706   0.00309816397705   0.66639257018370
   0.52153187784706   0.52222092886745   0.00206442294164   0.66633753310988
   0.52222092886745   0.52268024851408   0.00137537192125   0.66622584621954
   0.52268024851408   0.52298644064974   0.00091605227461   0.66603968022104
   0.52298644064974   0.52319055953961   0.00060986013895   0.66574818474416
   0.52319055953961   0.52332663450846   0.00040574124908   0.66530212939707
   0.52332663450846   0.52341735020372   0.00026966628023   0.66462623862714
   0.52341735020372   0.52347782611110   0.00017895058498   0.66360015357257
   0.52347782611110   0.52351814345040   0.00011847467760   0.66205247451647
   0.52351814345040   0.52354502354606   0.00007815733829   0.65969656871308
   0.52354502354606   0.52356294530766   0.00005127724264   0.65607713566020
   0.52356294530766   0.52357487500129   0.00003335548103   0.65049287595277
   0.52357487500129   0.52358285443287   0.00002142578741   0.64234682700063
   0.52358285443287   0.52358824904516   0.00001344635583   0.62757814086887
   0.52358824904516   0.52359153987740   0.00000805174353   0.59880488346504
   0.52359153987740   0.52359328110033   0.00000476091130   0.59128948639768
   0.52359328110033   0.52359630078870   0.00000301968837   0.63426688268604
   0.52359630078870   0.52359630078870                  0                  0
   0.52359630078870   0.52359630078870                  0                NaN

exit