# Alex Timonov’s Scholarly Pursuits

Dr Alex Timonov received his doctorate in Computational Mathematics in 1984 from the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, formerly the applied mathematics branch of the famous Steklov Mathematical Institute, Moscow. Since 1990, he is a Senior Scientific Fellow of the Russian Academy of Sciences certified by the Presidium of Academy. His research interests include differential geometry, harmonic analysis, numerical analysis, nonlinear PDEs, inverse problems and mathematical imaging.

**Monographs **

*Carleman Estimates for Coefficient Inverse Problems and Numerical Applications,* Brill Academic Publishers, VSP, Boston, Utrecht, 2004 (with M. V. Klibanov).

*Mathematical Problems of Computed Tomography, *Nauka, Moscow, 1987 (in Russian) (with A.N. Tikhonov and V.Ya. Arsenin).

**Recent External Research Grants **

“Regularizing algorithms for estimating the marine environments and surface ship signatures”, Swedish Defence Research Agency (FOI), Stockholm, Sweden, 2011 – 2014, Principal Investigator (pending).

“Globally convergent algorithms for solving inverse problems of marine electromagnetics and their applications”, Research grant, Swedish Defence Research Agency (FOI), Stockholm, Sweden, 2008-2009, Principal Investigator.

U.S. Army Research Laboratory (ARL) and U.S. Army Research Office (ARO) grant W911NF-05-0378 via UNC Charlotte/ARO, 2007, Principal Investigator.

4. “Millimeter-wave MEMS signal processing platform”, Canadian Strategic grant, National Science and Engineering Research Council, Canada, 2006-2009, Co-investigator.

**Selected Recent Presentations**

The 7^{th} International Conference on Marine Electromagnetics, “A New Approach: Multimodality Inverse Problems of Marine Electromagnetics”, Scripps Oceanographic Institute, UCSD, San-Diego, CA, June 20-23, 2011.

1053^{rd} American Mathematical Society Meeting, Special Session on Inverse Problems and Signal Processing, “New algorithms for reconstructing the conductivity from interior data”, Florida Atlantic University, Boca Raton, FL, October 30 – November 1, 2009.

Inverse Problems: Recent Progress and New Challenges, Banff International Research Station for Mathematical Innovation and Discovery (BIRS), “Numerical study of algorithms for reconstructing the conductivity from interior data”, Banff Centre, Alberta, Canada, November 16-21, 2008.

First International Congress on Applied Inverse Problems (AIP 2007), “A numerical study on the globally convergent convexification algorithms “, Vancouver, Canada, June 25-29, 2007.

International Symposium on Inverse Problems, Design and Optimization (IPDO 2007), “Quantitative millimetre-wave imaging via the globally convergent convexification algorithm“, Miami, FL, April 16-19, 2007.

**Selected Recent Papers**

Current Density Impedance imaging, Contemporary Mathematics, American Mathematical Society, 2011 (in press) (with A.Nachman and A.Tamasan)

Reconstruction of planar conductivities in subdomains from incomplete interior data, *SIAM** Journal on Applied Mathematics, 70(8), *2010, pp. 3342-3362 (with A.Nachman and A.Tamasan),.

Recovering the conductivity from a single measurement of interior data, *Inverse Problems, *25*, *2009, pp. 16 (with A.Nachman and A.Tamasan),

A new approach to acoustic frequency sounding of layered media, *Numerical Functional Analysis and Optimization,* 29(4-5), 2008, pp. 470-480 (with A.Tamasan),

Conductivity imaging with a single measurement of boundary and interior data, *Inverse Problems,* 23, 2007, pp.2551-2563 (with A.Nachman and A.Tamasan),

Numerical studies on the globally convergent convexification algorithm in 2D, *Inverse Problems, *23*, *2007, pp. 123-138 (with M.V.Klibanov).

Global uniqueness for a 3D/2D inverse conductivity problem via the modified method of Carleman estimates, *Journal of Inverse and Ill-Posed Problems, *13, 2005, pp. 149-174 (with M.V.Klibanov).

A new iterative procedure for the numerical solution of coefficient inverse problems, *Applied Numerical Mathematics*, 54, 2005, pp. 280-291 (with M.V.Klibanov).

A unified framework for constructing the globally convergent convexification algorithms for multidimensional coefficient inverse problems, *Applicable Analysis*, 83, 2004, pp. 933-955 (with M.V.Klibanov).

On the mathematical treatment of time reversal, *Inverse Problems,* 19, 2003, pp. 1299-1318 (with M.V.Klibanov).

A globally convergent convexification algorithm for the inverse problem of electromagnetic frequency sounding in one dimension, *Numerical Methods and Programming,* 4, 2003, pp. 52-81 (with M.V.Klibanov).

A sequential minimization algorithm based on the convexification approach, *Inverse Problems*, 19, 2003, pp. 331-354 (with M.V.Klibanov).

An efficient algorithm for solving the inverse problem of locating the interfaces using the frequency sounding data, *Journal of Computational Physics,* 183, 2002, pp.1-16 (with M.V.Klibanov).

A new slant on the inverse problems of electromagnetic frequency sounding: “Convexification” of a multiextremal objective function via the Carleman weight functions, *Inverse Problems,* 17, 2001, pp. 1865-1887 (with M.V.Klibanov).

Factorised preconditionings of successive approximations in finite precision, *BIT: Numerical Mathematics,* 41(3), 2001, pp. 582-598.