Notes—Chap. 10a Introduction to Numerical Methods
(pp. 405 – 413)
- Chapter presents program solutions to some mathematics and statistics
problems.
- We will cover first two sections
- Mathematics of Newton’s Method for finding solution to f(x) = 0:
- studied Bisection Method in section 5.6.
- Newton’s method usually converges to a solution faster
- Steps:
1. Start with a guess (or approximation), x0.
2. Compute new approximation from previous one using formula
f (xn)
xn+1 = xn - ───── (mathematically derived on p. 407)
f ’ (xn)
3. Continue computing new approximations until
a. | xn+1 - xn | < acceptable tolerance or
b. n = maximum number of iterations
- Show graphically (see Fig. 10.1, p. 407):
