منابع مشابه
On the DSM Newton-type method
A wide class of the operator equations F(u)= h in a Hilbert space is studied. Convergence of a Dynamical Systems Method (DSM), based on the continuous analog of the Newton method, is proved without any smoothness assumptions on the F ′(u). It is assumed that F ′(u) depends on u continuously. Existence and uniqueness of the solution to evolution equation u̇(t)=−[F ′(u(t))]−1(F (u(t))− h), u(0)= u...
متن کاملRamm DSM of Newton type
This paper is a review of the authors’ results on the DSM (Dynamical Systems Method) for solving operator equation (*) F (u) = f . It is assumed that (*) is solvable. The novel feature of the results is the minimal assumption on the smoothness of F . It is assumed that F is continuously Fréchet differentiable, but no smoothness assumptions on F ′(u) are imposed. The DSM for solving equation (*)...
متن کاملHow large is the class of operator equations solvable by a DSM Newton-type method?
It is proved that the class of operator equations F(y) = f solvable by a DSM (dynamical systems method) Newton-type method, u̇ = −[F (u) + a(t)I]−1[Fu(t) + a(t)u − f ], u(0) = u0, (∗) is large. Here F : X → X is a continuously Fréchet differentiable operator in a Banach space X , a(t) : [0, ∞) → C is a function, limt→∞ |a(t)| = 0, and there exists a y ∈ X such that F(y) = f . Under weak assumpti...
متن کاملOn a Newton-Type Method for Differential-Algebraic Equations
This paper deals with the approximation of systems of differential-algebraic equations based on a certain error functional naturally associated with the system. In seeking to minimize the error, by using standard descent schemes, the procedure can never get stuck in local minima but will always and steadily decrease the error until getting to the solution sought. Starting with an initial approx...
متن کاملA Newton-type method and its application
We prove an existence and uniqueness theorem for solving the operator equation F(x) + G(x)= 0, where F is a continuous and Gâteaux differentiable operator and the operator G satisfies Lipschitz condition on an open convex subset of a Banach space. As corollaries, a recent theorem of Argyros (2003) and the classical convergence theorem for modified Newton iterates are deduced. We further obtain ...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics and Computing
سال: 2011
ISSN: 1598-5865,1865-2085
DOI: 10.1007/s12190-011-0494-z