CHEN 3201 Lecture Notes - Lecture 21: Jacobian Matrix And Determinant, Taylor Series
8 Mar 2015
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Document Summary
Today: newton-raphson want to make residual vector go to 0. Method is the extension of newton"s method to n-dimensions. Reviewing newton"s method (1 dimension) f(x) = 0 make a taylor series expansion. To make this into a fixed point method. 3 things we did: made f(x) = 0 stopped it at 2nd term made x into xk+1. 3 steps: taylor series expansion, fixed point method, solved the form of the eqn has to be f(x) = 0 always calculate derivative analytically if possible --> keeps error low. Residual vector this is worst case scenario where all functions depend on all variables. In newton method, we expanded a single function by a single variable for newton-raphson, expand a lot of functions by a lot of variables. Taylor series expansion: if we just had 1 variable, then could stop at the x1 term each line is stuff for each individual eqn.
