Newton’s Method for Finding Solutions to Equations (VCE SSCE Mathematical Methods): Flashcards
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What Newton's method finds
What Newton's method finds
Approximate solutions to f(x) = 0
Newton's method iterative formula
Newton's method iterative formula
Critical condition for in Newton's method
Critical condition for in Newton's method
Must not equal zero
Geometric feature in Newton's method
Geometric feature in Newton's method
Tangent lines
Initial approximation symbol (Newton's method)
Initial approximation symbol (Newton's method)
Meaning of (Newton's method)
Meaning of (Newton's method)
Improved/next approximation
Convergence speed of Newton's method
Convergence speed of Newton's method
Typically very fast
Oscillating sequence (Newton's method)
Oscillating sequence (Newton's method)
Sequence bouncing between values, never converging
Effect when (Newton's method)
Effect when (Newton's method)
Tangent horizontal; method terminates
Factor affecting Newton's convergence speed
Factor affecting Newton's convergence speed
Choice of starting point