DMCA
How large is the class of operator equations solvable by a DSM Newton-type method?
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Alexander G. Ramm
| Citations: | 6 - 6 self |
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@MISC{Ramm_howlarge,
author = {Alexander G. Ramm},
title = { How large is the class of operator equations solvable by a DSM Newton-type method?},
year = {}
}
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Abstract
It is proved that the class of operator equations F (y) = f solvable by a DSM (Dynamical Systems Method) Newton-type method ˙u = −[F ′ (u) + a(t)I] −1 [F u(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 assumptions on F and a it is proved that This justifies the DSM (*). ∃!u(t) ∀t ≥ 0; ∃u(∞); F (u(∞)) = f.
