Tikhonov regularization by a reproducing kernel Hilbert space for the Cauchy problem for an elliptic equation. (English) Zbl 1185.65173

Takeuchi, Tomoya; Yamamoto, Masahiro

SIAM J. Sci. Comput. 31, No. 1, 112-142 (2008).

MSC:

65M30	Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations
46E22	Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Keywords:

Tikhonov regularization; Cauchy problem; reproducing kernel Hilbert space; ill-posed problem; stability; elliptic equation; convergence; numerical results