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$X_{k+1}=X_k-H(X_k)^{-1}*G(X_k)$

This is what I know to be a newton Raphson method. However, one of my hw question is asking about Modified Newton's method, and what we have learned in class is Quasi Newton's method .

Are Quasi & Modified same method but just different names? If not, can someone direct me for definitions of modified one please? I've been searching this quite a long time but didn't come to close answer.

Young Seo Kim
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    There are many variants of Newton's method, you might want to be more explicit about which one you mean? – copper.hat Jan 14 '22 at 21:26
  • @copper.hat Newton Raphson, Quasi Newton and Modified, if that helps? I'm sorry if Im unclear – Young Seo Kim Jan 14 '22 at 21:40
  • As far as I am aware, modified methods are for locating roots of multiplicity greater than one. Quasi Newton (variable metric) methods approximate the Hessian using various schemes (BFGS for example). Th term Newton Raphson is usually used for root finding, I believe. – copper.hat Jan 14 '22 at 21:46

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