### Dr Gaanutula Damodar Reddy

#### Interests

1. Inverse and Ill-posed Problems.
2. Regularization Methods.
3. Weighted Regularization Methods and its Parameter Choice rules.

### Experience

• January 2020 to July 2020: Assistant Professor, Dept. of Mathematics, IIIT Kottayam.
• April 2016 to December 2019: Post Doctoral Fellow, Mechanical Aerospace Engg. IIT Hyderabad.
• April 2015 to October 2015: Research Associate, Dept. of Mathematics, IISER Thiruvananthapuram.
• July 2010 to December 2010: Ad hoc Faculty, Dept. of MACS, NIT Surathkal Karnataka.

### Research Interest

• We study the a posteriori parameter choice rules for iterated Tikhonovregularization with operator-dependent semi-norms and obtain the optimal rate of convergence using these parameter choice rules.
• In many practical cases we cannot determine the noise level exactly, we propose a family of parameter choice rules to choose the regularization parameter for weighted regularization schemes with inexact noise level and discuss the convergence analysis of the scheme and subsequently establish the quasi optimality for the subfamily of parameter choice rules.
• This family of parameter choice rules edge over the parameter choice rules proposed by U. Hamarik et al.
• We investigate the new weighted regularization schemes along with the parameter choice rules for solving linear (bounded and unbounded) operator equations and discuss the convergence analysis of approximate solution and then establish the optimal rate of convergence.
• We seek the applicability of these schemes and the parameter choice rules in the context of Cauchy problem for the Helmholtz equation.

### Awards & Fellowships

• 2015—Post Doctoral Fellowship—NBHM.
• 2010—215th rank in GATE-2010—GATE.
• 2008—1st rank in M.Phil. Entrance Exam—Pondicherry University.
• 2007---1st rank in M.Sc. Entrance Exam—Pondicherry University.

### Publications

• Discrepancy Principles for fractional Tikhonov regularization method leading to optimal convergence rates, Santhosh George, G. D. Reddy, and K. Kanagaraj Journal of Applied Mathematics and Computing, (Accepted).
• A class of parameter choice rules for stationary iterated weighted Tikhonov regularization scheme, G. D. Reddy, Applied Mathematics and Computation, 347, 464-476 (2019).
• Computation of control for linear approximately controllable system using weighted Tikhonov regularization, Ravinder Katta, G. D. Reddy, and N. Sukavanam, Applied Mathematics and Computation, 317, 252-263 (2018).
• The parameter choice rules for weighted Tikhonov regularization scheme, G. D. Reddy, Computational and Applied Mathematics, 37, 2039-2051 (2018).
• A regularized iterative scheme for solving singularly perturbed elliptic PDE, M. P. Rajan and G. D. Reddy, Mathematics and Computers in Simulation, 144, 21-34 (2018).
• An iterative Tikhonov regularization for solving singularly perturbed elliptic PDE, M. P. Rajan and G. D. Reddy, Mediterranean Journal of Mathematics, DOI:10.1007/s00009-017-0980-0.
• An iterative technique for solving singularly perturbed parabolic PDE, M. P. Rajan and G. D. Reddy, Journal of Applied Mathematics and Computing, 50, 199-225 (2016).
• A variant of Tikhonov regularization for parabolic PDE with space derivative multiplied by a small parameter $\epsilon$, M. P. Rajan and G. D. Reddy, Applied Mathematics and Computation, 259, 412-426 (2015).

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