Necessary and sufficient conditions for the polynomial convergence of the quasi-reversibility and finite-difference methods for an ill-posed cauchy problem with exact data

作者：Kokurin M M^*

来源：Computational Mathematics and Mathematical Physics, 2015, 55(12): 1986-2000.

DOI：10.1134/S0965542515120076

• Cauchy problem for abstract equation
• sectorial operator
• Banach space
• ill-posed problem
• difference scheme
• quasi-reversibility method
• convergence rate
• interpolation of Banach spaces

The convergence of the quasi-reversibility method and two classes of finite-difference methods for solving the ill-posed Cauchy problem for the first-order equation with a sectorial operator in a Banach space is analyzed. The necessary and sufficient conditions-close to one another-for the convergence of these methods with a rate polynomial with respect to the regularization parameter or discretization step are obtained in terms of the exponent in the source representability of the solution.

• 出版日期2015-12