1
$\begingroup$

I'm new to numerical analysis, and have been learning root finding algorithms. I am a bit confused about the difference between Muller's method, and Newton's method using an n-degree interpolating polynomial.

How is the Muller's method, which approximates f(x) using a quadratic polynomial, different from the Newton's method, where lets say we use a 2 degree interpolating polynomial to find roots of f(x)?

I could not find clear and concise theory on using the Newton method with a 2 degree interpolating polynomial to identify if its the same as or is different than the Muller's method.

$\endgroup$
1
$\begingroup$

One of the most basic techniques in numerical analysis, when solving a complicated problem, is to construct an approximately-similar easy problem, solve that to obtain an approximate solution, and restart the process using that solution as a new starting point. This is a very general technique, and it’s not even restricted to root finding methods.

Newton’s and Halley’s methods both share this construction, but that’s not enough to call them the “same” method: most iterative methods are constructed this way. So picking which specific approximation (a line, a quadratic, etc) to use and how is what defines the method, not the general approach.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.