By simply transforming the quadratic matrix equation into an equivalent fixed-point equation, we construct a successive approximation method and a Newton’s method based on this fixed-point equation. Under suitable conditions, we prove the local convergence of these two methods, as well as the linear convergence speed of the successive approximation method and the quadratic convergence speed of ...

We consider two-dimensional overdamped double-well systems perturbed by white noise. In the weak-noise limit the most probable fluctuational path leading from either point attractor to the separatrix (the most probable escape path, or MPEP} must terminate on the saddle between the two wells. However, as the parameters of a symmetric double-well system are varied, a unique MPEP may bifurcate int...

We compute renormalization group fixed points and their spectrum in an ultralocal approximation. We study a case of two competing non-trivial fixed points for a three-dimensional real N -component field: the O(N)-invariant fixed point vs. the cubic-invariant fixed point. We compute the critical value Nc of the cubic φ -perturbation at the O(N)-fixed point. The O(N) fixed point is stable under a...