The philosophy of the approximate global convergence for multidimensional coefficient inverse problems

• Both the most important and the most challenging question in the numericaltreatment of a Multidimensional Coefficient Inverse Problem for a PDE is thefollowing: How to obtain a point in a small neighborhood of the exactsolution without any a priori knowledge of this solution? The recentnumerical experience of the authors for two types of MultidimensionalCoefficient Inverse Problems shows that in order to develop a trulyefficient algorithm addressing this question, it is necessary to make somereasonable approximations which cannot be rigorously justified.Nevertheless, numerical studies show that corresponding algorithms workquite well. The authors call this approach "approximateglobal convergence/reconstruction". The goal of the paper is to present ashort illustrative review of this philosophy.

Subject headings

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Keyword

philosophy

approximate global convergence

coefficient inverse problems

philosophy; coefficient inverse problems; approximate global convergence

Publication and Content Type

art (subject category)

ref (subject category)