Measures how accurately we can expect to be able to solve a problem, independently of the algorithm used
The BEST we can hope for
(assume for now that we can evaluate exactly at )
This estimates the number of decimal digits to which agree with
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% x = 0:1e-4:2
t = linspace(0, 2, 20001) % num from 0 to 2, 20001 points logt = log(t) % natural log function
plot(t, logt)
sint = sin(t) plot(t, sint) shg
t = linspace(0, pi, 10000) plot(t, sint)
ill condition: if condition number is > 1 well condition: if condition number <= 1
we don¡¯t have any correct digits, but answer is reasonable. Here, we are basically approximating 0 (y and yhat should be 0)
We say that an algorithm to compute f(x) is STABLE if it returns satisfying:
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