Regularized and preconditioned conjugate gradient like-methods methods for polynomial approximation of an inverse Cauchy problem

Sudad M. Rasheed (1) , Abdeljalil Nachaoui (2) , Mudhafar F. Hama (3) , Adil K. Jabbar (3)

1 Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah, Iraq
2 LMJL - Laboratoire de Mathématiques Jean Leray
3 Department of Mathematics, College of Science, University of Sulaimani, Sulaymaniyah, Iraq

In this paper, regularization combined with a preconditioning strategy is used to solve the ill-conditioned linear system obtained from the approximation of the inverse Cauchy problem for the Poisson equation in an arbitrary bounded domain. This approximation is based on the polynomial expansion (Liu & Kuo,2016). The presented numerical results show that the considered methods produced stable numerical solutions. More-over, the preconditioned regularization algorithms analyzed in this article require a very low computational effort, and that therefore represents another advantage of the numerical methods used to solve the Cauchy problem.

Mots clés: Inverse Cauchy problems; polynomial expansion; preconditionned linear systems; Conjugate Gra-dient like-methods.

Domaines: Mathématiques [math]; Analyse numérique [math.NA]

Sudad M. Rasheed, Abdeljalil Nachaoui, Mudhafar F. Hama, Adil K. Jabbar. Regularized and preconditioned conjugate gradient like-methods methods for polynomial approximation of an inverse Cauchy problem. Advanced Mathematical Models & Applications, 2021, 6 (2), pp.89-105. ⟨hal-03327195⟩