Images of Steepest Descent
 A few images of the number of iterations of steepest descent required to locate roots for three functions. These are in the style of [1]. The first image is of the behavior on the function
1k
which has one minimum. Color corresponds to the log of the number of iterations required. The second image is of
1k
which has 4 minimums; the colors correspond to the different basins of attraction. The last function is
1k
which has five basins of attraction shown.
858k
Steepest descent on f3
398k
Steepest descent on f4
342k
Steepest descent on f5
Scripts
  1. A J script steepest_descent_www.ijs to create the first image of this type.
  2. It requires raster5.ijs as well (installed in the fvj2 subdirectory of the J directory).

References
  1. Clifford A. Reiter, Visualizing Steepest Descent, The Visual Computer, 8 1 (1991), 64-67.