Secant Method
Objectives
 | secant method algorithm |
| strength and weaknesses of the method |
| interpretation of relative error |
Vocabulary
Super-linear rate of convergence
Concepts
| Approximation of derivative by difference quotient |
| Secant method including stopping criteria |
| Method properties: |
Method properties:
|
Strength |
Weaknesses |
|
Method requires evaluation of function but not derivative at each iteration |
Method needs two starting guesses |
|
Local, super-linear rate of convergence when approximation is close to root |
Convergence rate is not guaranteed when approximation is not close to the root |
|
Error estimate available under reasonable assumptions |
Method may converge very slowly or not at all |
|
Easier to implement than Newton's method |
Convergence rate is not as fast as that of Newton's method |
|
Two step secant method is competitive with one Newton's iteration |
Stopping criteria choice not obvious |
|
May be used to find complex roots |
Requires initial guess to be complex in order to find a complex root |
|
Method may be extended to higher dimension |
Requires to solve a different large system of linear equation at each iteration |