At least I know the method I explained worked for a relatively simple case, as it gave the same result as another root-finding scheme. Table 1 shows the iterated values of the root of the equation. Let E be the k-dimensional vector space with the Euclidean norm x (x, x)/2. diverging away from the root in ther NewtonRaphson method.-For example, to find the root of the equation. I was given a piece of Matlab code by a lecturer recently for a way to solve simultaneous equations using the Newton-Raphson method with a jacobian matrix (Ive also left in his comments). Or maybe I am mistaken and it has nothing to do with Newton-Raphson. The Newton-Raphson method is very popular also in the multidimensional case (here we have far less methods to choose from). An implicit function theorem and a resulting modified Newton-Raphson. To be more clear, I have a vector $\pmb)$), it would be pretty awkward I think. Can I use this information to ensure the convergence of my solution? What if I have a vector function which I want to finds its roots (each root depending on the other roots), but I know that the true roots have the same sign as my initial guess, and that it must stay that way in every step of the iteration procedure in order that the solution doesn't become irretrievable. With scalar functions it is easy to construct a mixed Newton-Raphson-bisection algorithm so that the solution always stays inside the given bounds in which it is bracketed.
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