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Jun 18, 2011 · yuck r for loop really makes me feel antsy. sapply, lapply are also almost as slow. john chambers wrote a warning in his R book that vectorization is much faster because the operation becomes truly linear. if you use for loop to implement something that should be linear, the whole operation becomes O(n^2), which is quite sad.

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Newton-Raphson Method in R Yin Zhao [email protected] January 2014 1 Newton-Raphson Method Let f (x) be a differentiable function and let a 0 be a guess for a solution to the equation f (x) = 0 We can product a sequence of points x = a 0, a 1, a 2,... via the recursive formula f (a n) a n+1 = a n − f 0 (a n) that are successively better approximation of a solution to the equation f (x) = 0.

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MATLAB Programming Tutorial #27 Newton-Raphson (multi Variable)Complete MATLAB Tutorials @ https://goo.gl/EiPgCF

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itatively but is essential and a limitation to the convergence of Newton’s method. This is usually coined as the local quadratic convergence. Remark 1.6. The Newton’s method is also refereed as Newton-Raphson method; see [1] on ‘who is Raphson’? 2. NEWTON-TYPE METHODS The constraint of Newton’s method are: (1)Require a good initial guess.

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Multivariate Newton-Raphson Univariate root ﬁnding: suppose we want to ﬁnd a root of f : R ! R. Start at some x0, xn+1 = xn f(xn) f0(xn); n 0: Multivariate root ﬁnding: suppose we want to ﬁnd roots of f : Rp! Rp fx 2 Rp: f(x) = 0 2 Rpg: Start at some x0 xn+1 = xn Jf(xn) 1f(x n); n 0: where Jf is the Jacobean of f.

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3.3 The Newton Raphson Algorithm in k Dimensions Suppose we want to ﬁnd the xˆ ∈Rk that maximizes the twice continuously diﬀerentiable function f : Rk →R. Recall f(x+h) ≈a+b0h+ 1 2 h0Ch where a = f(x), b = ∇f(x), and C = D2f(x). Note that C will be symmetric. This implies ∇f(x+h) ≈b+Ch. Once again, the ﬁrst order condition for a maximum is