Mathematics · Numerical Analysis
Fix a α ∈ (0, 1). Consider the iteration defined by: x k+1 = 1 2 (x k 2 + α), k = 0, 1, 2, ... The above iteration has two distinct fixed points ζ 1 and ζ 2 such that 0 1 2 . Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If - ζ 2 0 ≤ 0, then lim k→∞ x k = ζ 1 .
- 2If 0 ≤ x 0 2 , then lim k→∞ x k = ζ 1 .✓
- 3The iteration is equivalent to the recurrence relation x k+1 - ζ 1 = 1 2 (x k + ζ 2 )(x k - ζ 1 ).
- 4The iteration is equivalent to the recurrence relation x k+1 - ζ 1 = 1 2 (x k + ζ 1 )(x k - ζ 1 ).
Correct answer
If 0 ≤ x 0 2 , then lim k→∞ x k = ζ 1 .
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