Example 7.  Use the Taxi-Cab method to find the minimum of   [Graphics:Images/PowellMethodMod_gr_217.gif].  
Use the modified program listed above that includes graphics commands to draw the vertices and edges used in finding the solution.

Solution 7.

Enter the function  [Graphics:../Images/PowellMethodMod_gr_218.gif] and graph the surface [Graphics:../Images/PowellMethodMod_gr_219.gif].

[Graphics:../Images/PowellMethodMod_gr_17.gif]

[Graphics:../Images/PowellMethodMod_gr_18.gif]

[Graphics:../Images/PowellMethodMod_gr_19.gif]
[Graphics:../Images/PowellMethodMod_gr_20.gif]

[Graphics:../Images/PowellMethodMod_gr_21.gif]

[Graphics:../Images/PowellMethodMod_gr_22.gif]
[Graphics:../Images/PowellMethodMod_gr_23.gif]

[Graphics:../Images/PowellMethodMod_gr_24.gif]

[Graphics:../Images/PowellMethodMod_gr_25.gif]



[Graphics:../Images/PowellMethodMod_gr_222.gif]



[Graphics:../Images/PowellMethodMod_gr_223.gif]
[Graphics:../Images/PowellMethodMod_gr_224.gif]
[Graphics:../Images/PowellMethodMod_gr_225.gif]
[Graphics:../Images/PowellMethodMod_gr_226.gif]



[Graphics:../Images/PowellMethodMod_gr_227.gif]


[Graphics:../Images/PowellMethodMod_gr_228.gif]

[Graphics:../Images/PowellMethodMod_gr_229.gif]

[Graphics:../Images/PowellMethodMod_gr_230.gif]

[Graphics:../Images/PowellMethodMod_gr_231.gif]

[Graphics:../Images/PowellMethodMod_gr_232.gif]

[Graphics:../Images/PowellMethodMod_gr_233.gif]

[Graphics:../Images/PowellMethodMod_gr_234.gif]

[Graphics:../Images/PowellMethodMod_gr_235.gif]

[Graphics:../Images/PowellMethodMod_gr_236.gif]

[Graphics:../Images/PowellMethodMod_gr_237.gif]

[Graphics:../Images/PowellMethodMod_gr_238.gif]

[Graphics:../Images/PowellMethodMod_gr_239.gif]

[Graphics:../Images/PowellMethodMod_gr_240.gif]

[Graphics:../Images/PowellMethodMod_gr_241.gif]

Animation 1.  ( Powell's Method  Powell's Method  ).  Internet hyperlink.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004