Example 3.2
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Consider the system f(x,y) = {x2 + y2 - 1, x + y2 - 1}
with Newton-invariant set x - y - 1 = 0. We construct the randomized system
gR(x,y) = {x2 + y2 - 1 + 2(x - y - 1), x + y2 - 1 + 3(x - y - 1)}
and take start points (1/250,-249/250) and (251/250,-1/250). Since both quadratically converge
to solutions of gR = 0 and start on this Newton-invariant set, Theorem 3.1 yields
the limit points are indeed solutions of f = 0. Note that one of the solutions, namely (1,0), is a singular solution with respect to f.
The remainder of this page documents this computation.
Directions
Before you begin, you will need to have a working version of alphaCertified.
- Save the files system and points in the same directory.
- Execute the command
>> alphaCertified system points
from the directory.
- Here is the output displayed to the screen. This shows that both are approximate solutions of gR = 0.
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