Successive Numeric Approximation
Terminology
successive numeric approximation
: solving a mathematical problem using a numeric algorithm that estimates a solution
convergence
: does the algorithm produce the correct answer? is each estimate better than the previous
rate of convergence
: how fast does the algorithm converge?
error
: | approximate_value - exact_value |
percentage error
: | error / exact_value | × 100%
estimated error
: | estimate
n+1
- estimate
n
|
step size (h)
order of accuracy
: indication of how fast we converge
If the step size is halved, the error is reduced by a factor of:
O(h)
O(h
2
)
O(h
3
)
Finding roots
Find the value(s) of
x
such that
f
(
x
) = 0
Bisection Method
Newton's Method
See
Finding roots
for example and implementation