Match the following iterative methods for solving algebraic equations and…
2006
Match the following iterative methods for solving algebraic equations and their orders of convergence.
- A.
I-R, II-S, III-P, IV-Q
- B.
I-S, II-R, III-Q, IV-P
- C.
I-S, II-Q, III-R, IV-P
- D.
I-S, II-P, III-Q, IV-R
Show answer & explanation
Correct answer: D
The standard orders of convergence for these methods are:
Bisection method: The interval is halved at every iteration, so it gains 1 bit of accuracy per iteration. Hence I → S.
Newton-Raphson method: Near a simple root, it has quadratic convergence, so its order is 2. In some special cases the order may be higher. Hence II → P.
Secant method: Its order of convergence is approximately 1.62. Hence III → Q.
Regula Falsi method: It is linearly convergent in the usual case. Hence IV → R.
Therefore, the correct matching is I-S, II-P, III-Q, IV-R.