Consider the following iterative root-finding methods and convergence…
2004
Consider the following iterative root-finding methods and convergence properties.
Methods:
(Q) False Position
(R) Newton-Raphson
(S) Secant
(T) Successive Approximation
Convergence properties:
(I) Order of convergence = 1.62
(II) Order of convergence = 2
(III) Order of convergence = 1 with guarantee of convergence
(IV) Order of convergence = 1 with no guarantee of convergence
Which of the following is the correct matching?
- A.
Q-III R-IV S-II T-I
- B.
Q-III R-II S-I T-IV
- C.
Q-II R-I S-IV T-III
- D.
Q-I R-IV S-II T-III
Show answer & explanation
Correct answer: B
Match each method with its standard convergence property. False Position is a bracketing method, so it has order 1 with guarantee of convergence: Q-III. Newton-Raphson has quadratic convergence near a simple root: R-II. Secant method has order of convergence about 1.62: S-I. Successive Approximation or fixed point iteration is generally order 1 and convergence is not guaranteed unless the iteration satisfies the required contraction condition: T-IV. Therefore the correct matching is Q-III R-II S-I T-IV.