It is well known that a damped or underrelaxed Newton's method will sometimes solve a system of nonlinear equations when the full Newton's method cannot. This happens, for example, when only a poor ...

C. C. Paige, M. A. Saunders, Solution of Sparse Indefinite Systems of Linear Equations, SIAM Journal on Numerical Analysis, Vol. 12, No. 4 (Sep., 1975), pp. 617-629 ...

There are two correct ways to solve it. The first way to find the solution is to add the equation, then combine the sum with that of the previous equation.

For instance, no mathematical method exists that can reliably tell whether any given Diophantine equation has solutions. According to Booker, the sum-of-three-cubes problem “is one of the simplest” of ...