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kriukov / interval-methods

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Krawczyk1D and 2D "maybe a zero" under certain conditions #8

Open kriukov opened 9 years ago

kriukov commented 9 years ago

Both 1D and 2D Krawczyk returns "maybe a zero" instead of "unique zero" when we start with the interval at whose midpoint the derivative is 0, but it turns out that the affecting side are functions, not intervals (changing the intervals doesn't help).

Examples: using KrawczykMethod f(x) = (x - 2)^2 a = Interval(1, 3) # or another interval krawczyk(f, a)

Increase in precision doesn't help.

Another example: using KrawczykMethod2D f(x) = [(x[1] - 2)^2, (x[2] - 3)^2] a = [Interval(1, 3), Interval(2, 4)] # or another set of intervals krawczyk2d(f, a)

kriukov commented 9 years ago

Krawczyk1D: putting "x^2 - 4x + 4" instead of "(x - 2)^2" doesn't even return "maybe". Degenerate roots?

dpsanders commented 9 years ago

I am surprised about "x^2 - 4x + 4", but indeed degenerate roots cannot be identified by this kind of method. (Actually, I don't see how any method could identify them accurately.)