Stability of the numerical method for solving the 3 ~ inverse scattering problem with fixed - energy data

Let IA,(B'B)-A(@', @)I < 6, where 6 > 0 is a small given number, A(@', 8) is the unknown scattering amplitude at a fixed k > 0 corresponding to a potential q(x)EL2(Bu), q(x) = q(x), q(x) = 0 in a,:= R'\B,, Bo:= {x: 1x1 < a } , @ ' , B E S 2 , the unit sphere. Functions qa(x) are constructed, given S z 0 and the function A,(@',@), such that 11%-q/IL2(B,) 4 0 as 6 4 0. The function A,(B', 0) is not a scattering amplitude but is a measurement of the scattering amplitude, i.e. the noisy scattering data.