← Main book chapter 2
Contents / index
Browser back
← Previous chapter
Next chapter →
Laboratory
Memory
Cards
Sort
Match
Visuals
Coding
Quiz
Game Cards
Game Cards — Chapter 2
Each card is a fast recall challenge. Try to answer before revealing the back.
Shuffle on page
Reveal all
Hide all
Go to memory cards
Hybrid methods
Practical solvers often combine bracketing safety with Newton or secant speed.
Bisection
Bisection is globally reliable under a sign change. It is linearly convergent and preserves a bracket at every step.
Newton method
Newton is locally quadratic for a simple root if the start is close enough and \(f'\) is not zero near the root.
Root-finding problem
Solve \(f(x)=0\). A complete answer needs assumptions, starting data, stopping rule, residual, and error interpretation.
Multiple roots
Multiple roots slow Newton's method. Multiplicity correction can restore fast convergence when the multiplicity is known.
Fixed-point iteration
The iteration \(x_{n+1}=g(x_n)\) converges locally when \(|g'(x_\ast)|<1\).
Secant method
The secant method avoids derivatives and is superlinear, but it does not preserve a bracket.