Continuous dependence of least squares solutions of linear boundary value problems

Abstract:

Let ${u_\lambda }$ be the unique least squares solution of minimal norm of the linear boundary value problem $Lu - \lambda u = f$, where $L$ is a selfadjoint differential operator in ${L^2}[a,b]$. Working in the Sobolev space ${H^n}[a,b]$, the alternative method is used to examine the continuous dependence of the ${u_\lambda }$ on the parameter $\lambda$ as $\lambda \to {\lambda _0}$, and the convergent and divergent cases are both characterized.