GATE MA concept:fixed-point-iteration PYQs & Answers

Questions 1–3 of 3. Imported answers require independent review unless marked reviewed.

To find a real root of the equation

in the interval

by using the fixed-point iteration scheme, consider the following two statements:

S1: The iteration scheme

, converges for any initial guess

S2: The iteration scheme

, diverges for some initial guess

Then, which one of the following is correct?

Your answerChoose one option.

S1 is TRUE and S2 is FALSE

S2 is TRUE and S1 is FALSE

both S1 and S2 are TRUE

neither S1 nor S2 is TRUE

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

be the two fixed points of the function

, where

. For

, let the sequence

be generated by the fixed point iteration

Which one of the following is/are correct?

Your answerSelect all correct options. You can choose more than one.

converges to

for any

converges to

for any

converges to

for any

converges to

for any

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider the fixed-point iteration

with

and the initial approximation

Then, the order of convergence of the fixed-point iteration method is

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE MA concept:fixed-point-iteration PYQs