Tikhonov regularization of a nonhomogeneous first-order evolution equation

Regularization for a Laplace Equation with Nonhomogeneous Neumann Boundary Condition

We consider the following problem  uxx + uyy = 0, (x, y) ∈ (0, π)× (0, 1) u(0, y) = u(π, y) = 0, y ∈ (0, 1) uy(x, 0) = g(x), 0 < x < π u(x, 0) = φ(x), 0 < x < π The problem is shown to be ill-posed, as the solution exhibits unstable dependence on the given data functions. Using the new method, we regularize of problem and obtain some new results. Some numerical examples are given to illu...

Tikhonov Regularization

An important issue in quantitative nance is model calibration. The calibration problem is the inverse of the pricing problem. Instead of computing prices in a model with given values for its parameters, one wishes to compute the values of the model parameters that are consistent with observed prices. Now, it is well-known by physicists that such inverse problems are typically ill-posed. So, if ...

Tikhonov Regularization for an Integral Equation of the First Kind with Logarithmic Kernel

In this paper, we discuss stability and Tikhonov regularization for the integral equation of the rst 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.

A Regularization Parameter for Nonsmooth Tikhonov Regularization

In this paper we develop a novel criterion for choosing regularization parameters for nonsmooth Tikhonov functionals. The proposed criterion is solely based on the value function, and thus applicable to a broad range of functionals. It is analytically compared with the local minimum criterion, and a posteriori error estimates are derived. An efficient numerical algorithm for computing the minim...

Calibration of POD reduced-order models using Tikhonov regularization