4 problems

Let $g$ be a polynomial of degree $d\geq 2$ with coefficients in a number field $K$, and let $y_0\in K$. Define the Newton map … and, for each $n\geq 0$, set $y_{n+1}=N(y_n)$. Assu…

Neural-network Newton convergence conjecture. Newton's method, as given by the Newton inversion step, is locally convergent if the points $(\vec{\beta}_j\neq 0,\theta_j)$ are pairw…

Sparse-solution Newton conjecture. Newton's method is still convergent for such sparse solutions, and this convergence can also be proved.

Let $Y_{n,m}(t)$ be the sequence of functions used to generate the approximations, and define … The roots generated by this sequence are the zeros $y_n$ of the corresponding functi…