A. G. Ramm

activity

20012005

most citedOn the discrepancy principle

14 citations · 19 across the 5 of their papers we have counts for

collaborators

Showing math-phShow all

4 papers · 1 filter

math-ph2003★ 14 cited

On the discrepancy principle

A. G. Ramm

A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under sui…

math-ph2001

An inverse problem for an abstract evolution equation

S. V. Koshkin, A. G. Ramm

The inverse problem of finding the coefficient $\g$ in the equation $\dot{u}=A(t)u+\g(t)u+f(t)$ from the extra data of the form $ϕ (t) = u (t), w$ is studied. The problem is reduced to…

math-ph2001

Reconstruction of the potential from I-function

A. G. Ramm

If $f (x, k)$ is the Jost solution and $f (x) = f (0, k)$ , then the $I$ -function is $I (k) := \frac{f ^{'} ( 0 , k )}{f ( k )}$ . It is proved that $I (k)$ is in one-to-one correspondence with t…

math-ph2001

An inverse problem for the heat equation

A. G. Ramm

Let $u_{t} = u_{xx} - q (x) u, 0 \leq x \leq 1$ , $t > 0$ , $u (0, t) = 0, u (1, t) = a (t), u (x, 0) = 0$ , where $a (t)$ is a given function vanishing for $t > T$ , $a (t) \neq \equiv 0$ , $\int^T_0…