Newton’s method near a simple root converges:
Error Analysis for Iterative Methods
Order of convergence (linear vs. quadratic, asymptotic error constant), multiple roots and the modified Newton method.
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2.4
1. Order of Convergence of a Sequence
Order of Convergence
Exam angle
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2.4 Exercise-7(a)
2.4 Exercise-8(a)
2.4 Exercise-8(b)
Exercise 2.4
Modified N ewton’s Method
Notes
At a multiple root Newton is only linear; modified Newton uses μ = f/f′: pₙ = pₙ₋₁ − f f′/((f′)² − f f″).
• Use Modified Newton’s method to find solutions accurate to
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