Question

When does Newton-Raphson method fail?​

Answer 1

Answer:

Newton's method will fail in cases where the derivative is zero. When the derivative is close to zero, the tangent line is nearly horizontal and hence may overshoot the desired root (numerical difficulties).

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Answer 2

$✰Answer:$

Newton's method will fail in cases where the derivative is zero. When the derivative is close to zero, the tangent line is nearly horizontal and hence may overshoot the desired root (numerical difficulties).

Other conditions for Newton Raphson to fail is-

a. If the tangent drawn from the point on the curve never meets the X axis (that is, the tangent becomes parallel to X axis)

b. If the function is not a Continuous function

c. If the function is not differentiable.[ Note that Newton Raphson uses differentiation.]

d. The derivatives tends to zero. See that there is a f’(Xn) term in the RHS of the Newton raphson equation. If this tends to 0, then the value of RHS tends to infinity (As anything divided by 0 is infinity).

e. The initial guess made for the root is so bad.