3 ms·
Nope. Easy counterexample: f1 = x^2 + 2x (roots: 0, -2) f2 = -x - 1 (root: -1) (f1 + f2) / 2 has one root which is 0.618 (the golden ratio) Now y
by willchang 19y ago
Nope. Easy counterexample:
f1 = x^2 + 2x (roots: 0, -2)
f2 = -x - 1 (root: -1)
(f1 + f2) / 2 has one root which is 0.618 (the golden ratio)
Now you have to tell us what your idea was.
- aswanson 19y agoThose original functions roots are not bounded by 1.
- pixcavator 19y agoReplace each x with 2x.
- willchang 19y ago[A real polynomial P is said to be stable if all its roots lie in the left half-plane.](http://mathworld.wolfram.com/StablePolynomial.html http://mathworld.wolfram.com/StablePolynomial.html) What's your definition of stable?
- aswanson 19y agoI meant the z-plane not s plane but it doesn't matter.