Say you are given $c\in R^n$ and want to find $x \in R^n$ so that $x^TAx+Bx=c$, where A is diagonal and B is full. Is there some method which converges faster or has less computation time than the standard Newton's method?
In general, the equation would be $A [f(x_1); f(x_2);...f(x_n)] +Bx=c$.
Context: I'm working on a collocation scheme for $u_t+f(u)_x=0$ that diagonalizes the nonlinear $f(u)_x$ term.