Furthermore, because T is smooth and tangent to the orbits, it must be the zero vector at the singular points.
This seems like a relevant quantity here since this vector will be the zero vector for networks 11, 12 and 13 but not for networks 9 and 10.
A null vector is a vector with norm zero, and in a Euclidean space such a vector would have to be the zero vector that could not be used to denote a great variety of points.
Theorem 4.1 Let H 1 and H 2 be two real Hilbert spaces and θ i be the zero vector of H i for i = 1, 2. Let A : H 1 → H 2 be a bounded linear operator with its adjoint B and U : H 1 → H 1 be a Lipschitzian accretive mapping with Lipschitz constant L > 0 and U − 1 ( θ 1 ) ≠ ∅.
Corollary 4.2 Let H 1 and H 2 be two real Hilbert spaces and θ i be the zero vector of H i for i = 1, 2. Let A : H 1 → H 2 be a bounded linear operator with its adjoint B. Let U : H 1 → H 1 be a Lipschitzian accretive mapping with Lipschitz constant L > 0 and U − 1 ( θ 1 ) ≠ ∅.
In our implementations, the initial point is chosen to be the zero vector and the stopping criterion for the nonlinear MHSS-like and HSS-like methods is frac{Vert b+vert x^{ k)}vert -Ax^{ k)}Vert _{2}}{Vert bVert _{2}}leq10^{-6 _{2}}leq10^{-6
