Tikhonov regularization for an integral equation of the first kind with logarithmic kernel
- Bruckner, Gottfried
- Cheng, Jin
2010 Mathematics Subject Classification
- 45A05 65R30
- integral equation of the first kind, analytic kernel, Tikhonov regularization, convergence rate
In this paper, we discuss stability and Tikhonov regularization for the integral equation of the first kind with logarithmic kernel. Since the kernel is analytic in our case, the problem is severely ill-posed. We prove a convergence rate for the regularized solution and describe a method for its numerical calculation.
- J. Inverse Ill-posed Problems, 8(2000), pp. 1-11