M.T. Nair & D. Shylaja. Conforming and nonconforming finite element methods for biharmonic inverse source problem, Inverse Problems 38 (2022), no. 2, Paper No. 025001, 36 pp.
P. Mathe, M.T. Nair & B. Hofmann, Regularization of linear ill-posed problems involving multiplication operators, Appl. Anal. 101 (2022), no. 2, 714–732.
M.T. Nair, Regularization of ill-posed operator equations: An overview, J. Anal. 29 (2021), no. 2, 519–541.
S. Mondal & M.T. Nair, On regularization of a source identification problem in a parabolic PDE and its finite dimensional analysis , J. Part. Diff. Eq., Vol. 34, No. 3, pp. 240-257
S. Mondal & M.T. Nair, Identification of matrix diffusion coefficients in a parabolic PDE, Comput. Methods Appl. Math., Nov. 30, 2021. https://doi.org/10.1515/cmam-2021-0061
M.T. Nair, On truncated spectral regularization for an ill-posed evolution equation, Proc. Indian Acad. Sci. Math. Sci. 131 (2021), no. 2, Paper No. 30, 11 pp.
S. Mondal & M.T. Nair, A linear regularization method for a parameter identification problem in heat equation, J. Inverse Ill-Posed Probl. 28 (2020), no. 2, 251–273. https://doi.org/10.1515/jiip-2019-0080
K. Jayakumar & M.T. Nair, Fourier truncation method for the non homogeneous time fractional backward heat conduction problem, Inverse Probl. Sci. Eng. 28 (2020), no. 3, 402–426. https://doi.org/10.1080/17415977.2019.1580707
A. Jana & M.T. Nair, A truncated spectral regularization method for a source identification problem, J. Anal. 28 (2020), no. 1, 279–293. https://doi.org/10.1007/s41478-018-0080-y
A. Jana & M.T. Nair, Truncated spectral regularization for an ill-posed non-linear parabolic problem, Czechoslovak Math. J. 69(144) (2019), no. 2, 545–569.
M. Nair, N. Sukavanam & R. Katta, Computation of control for linear approximately controllable system using Tikhonov regularization, Numer. Funct. Anal. Optim. 39 (2018), no. 3, 308–321. https://doi.org/10.1080/01630563.2017.1361440
M.T. Nair, A discrete regularization method for Ill-posed operator equations, J. Anal. 25 (2017), no. 2, 253–266.
S. George & M.T. Nair, A derivative-free iterative method for nonlinear ill-posed equations with monotone operators, J. Inverse Ill-Posed Probl. 25 (2017), no. 5, 543–551. https://doi.org/10.1515/jiip-2014-0049
M.T. Nair & S.D. Roy, A linear regularization method for a nonlinear parameter identification problem, J. Inverse Ill-Posed Probl. 25 (2017), no. 6, 687–701. https://doi.org/10.1515/jiip-2015-0091
A. Jana and M.T. Nair, Quasi-reversibility method for an ill-posed non-homogeneous parabolic problem, Numer. Funct. Anal. Optim. 37 (2016), no. 12, 1529–1550. https://doi.org/10.1080/01630563.2016.1216448
M.T. Nair, Compact operators and Hilbert scales in ill-posed problems, Math. Student 85 (2016), no. 1-2, 45–61.
A. Jana & M.T. Nair, Truncated spectral regularization for an ill-posed non-homogeneous Parabolic Problem, J. Math. Anal. Appl. 438 (2016), no. 1, 351–372.
M.T. Nair, Morozov-type discrepancy principle for nonlinear illposed problems under η-condition, Proc. Indian Acad. Sci. Math. Sci. 125 (2015), no. 2, 227–238.
M.T. Nair, A unified treatment for Tikhonov regularization using a general stabilizing operator, Anal. Appl. (Singap.) 13 (2015), no. 2, 201–215. https://doi.org/10.1142/S0219530514500122
P. Mahale & M.T. Nair, Lavrentiev regularization of nonlinear illposed equations under general source condition, J. Nonlinear Anal. Optim. 4 (2013), no. 2, 193–204.
K.P. Deepesh, S.H. Kulkarni & M.T. Nair, Approximation numbers for relatively bounded operators, Funct. Anal. Approx. Comput. 5 (2013), no. 2, 35–42. file:///Users/mtnair/Downloads/173-953-1-PB.pdf
Hui Cao & M.T. Nair, A fast algorithm for parameter identification problems based on multilevel augmentation method, Comput. Methods Appl. Math. 13 (2013), no. 3, 349–362. https://doi.org/10.1515/cmam-2013-0009
M.T. Nair, Quadrature based collocation methods for integral equations of the first kind, Adv. Comput. Math. 36 (2012), no. 2, 315–329. https://doi.org/10.1007/s10444-011-9196-1
M.T. Nair & P. Ravishankar, A generalization of continuous regularized Gauss-Newton method for ill-posed problems, J. Inverse Ill-Posed Probl. 19 (2011), no. 3, 473–510. https://doi.org/10.1515/jiip.2011.040
P. Mahale & M.T. Nair, Iterated Lavrentive regularization for nonlinear ill-posed problems, ANZIAM J. 51 (2009), no. 2, 191–217.
K.P. Deepesh, S.H. Kulkarni & M.T. Nair, Approximation numbers of operators on normed linear spaces, Integral Equations Operator Theory 65 (2009), no. 4, 529–542.
P. Mahale & M.T. Nair, Simplified generalized Gauss Newton method for nonlinear ill-posed problems, Math. Comp. 78 (2009), no. 265, 171–184.
M.T. Nair, On Morozov’s discrepancy principle for nonlinear ill-posed equations, Bull. Aust. Math. Soc. 79 (2009), no. 2, 337–342. doi:10.1017/S0004972708001342
M.T. Nair, On regularization of compact operator equations, J. Anal. 16 (2008), 67–80.
S.H. Kulkarni, M.T. Nair & G. Ramesh, Some properties of unbounded operators with closed range, Proc. Indian Acad. Sci. Math. Sci. 118 (2008), no. 4, 613–625.
M.T. Nair & U. Tautenhahn, Convergence rates for Lavrentievtype regularization in Hilbert scales, Comput. Methods Appl. Math. 8 (2008), no. 3, 279–293.
M.T. Nair & P. Ravishankar, Regularized versions of continuous Newton’s method and continuous modified Newton’s method for under general source conditions, Numer. Funct. Anal. Optim. 29 (2008), no. 9-10, 1140–1165.
S. George & M.T. Nair, A modified Newton-Lavrentiev regularization for nonlinear ill-posed Hammerstein-type operator equations, J. Complexity 24 (2008), no. 2, 228–240.
P. Mahale & M.T. Nair, Tikhonov regularization of nonlinear ill-posed equations under general source conditions, J. Inverse Ill-Posed Probl. 15 (2007), no. 8, 813–829.
M.T. Nair & S. Pereverziev, Regularized collocation method for Fredholm integral equations of the first kind, J. Complexity 23 (2007), no. 4-6, 454–467.
P. Mahale & M.T. Nair, General Source Conditions for Non-Linear Ill-Posed Equations, Numer. Funct. Anal. Optim. 28 (2007), no. 1-2, 111–126.
S.H. Kulkarni, M.T. Nair & M.N.N. Namboodiri, An elementary proof for a characterisation of *-isomorphisms, Proc. Amer. Math. Soc. 134 (2006), no. 1, 229–234.
M.T. Nair, On improving error estimates for Tikhonov regularization using an unbounded operator, J. Anal. 14 (2006), 143–157.
M.T. Nair, S. Perverziev & U. Tautenhahn, Regularization in Hilbert scales for under general smoothing conditions, Inverse Problems 21 (2005), no. 6, 1851–1869.
M.T. Nair, Eigenpairs of perturbed matrices, J. Anal. 12 (2004), 171–181.
M.T. Nair & Shinelal, Finite dimensional realization of mollifier method for compact operator equations, Math. Comp. 74 (2005), no. 251, 1281–1290.
M.T. Nair & Shinelal, Finite dimensional realization of mollifier method: A new stable approach, J. Inverse Ill-Posed Probl. 12 (2004), no. 6, 637–653.
M.T. Nair & U. Tautenhahn, Lavrentiev’s regularization under general source conditions, Z. Anal. Anwendungen 23 (2004), no. 1, 167–185.
S. George & M.T. Nair, Optimal order-yielding discrepancy principle for simplified regularization Hilbert scales: Finite dimensional realizations, Int. J. Math. Math. Sci. 2004, no. 37-40, 1973–1996.
S. George & M.T. Nair, An optimal order-yielding discrepancy principle for simplified regularization of ill-posed problems in Hilbert scales, Int. J. Math. Math. Sci. 2003, no. 39, 2487–2499.
M.T. Nair, E. Schock & U.Tautenhahn, Morozov’s discrepancy principle under general source conditions, Z. Anal. Anwendungen 22 (2003), no. 1, 199–214.
M.T. Nair & E.Schock, On the Ritz method and its generalization for ill-posed equations with non-self adjoint operators, Int. J. Pure Appl. Math. 5 (2003), no. 2, 119–134.
M.T. Nair & M.P. Rajan, Generalized Arcangeli’s discrepancy principles for a class of regularization methods for solving ill–posed problems, J. Inverse Ill-Posed Probl. 10 (2002), no. 3, 281–294.
M.T. air, Multiplicities of an eigenvalue: Some observations, Resonance, (12) (2002) 31–41.
M.T. Nair, Optimal order results for a class of regularization methods using unbounded operators, Integral Equations Operator Theory 44 (2002), no. 1, 79–92.
M.T. Nair & M.P. Rajan, Arcangeli’s type discrepancy principles for a class of regularization methods using a modified projection scheme, Abstr. Appl. Anal. 6 (2001), no. 6, 339–355.
M.T. Nair & M.P. Rajan, On improving accuracy for Arcangeli’s method for solving ill–posed equations, Integral Equations Operator Theory 39 (2001), no. 4, 496–501.
M.T. Nair & M.P. Rajan, Arcangeli’s discrepancy principle for a modified projection scheme for ill–posed problems, Numer. Funct. Anal. Optim. 22 (2001), no. 1-2, 177–198.
M.T. Nair, An iterative procedure for solving Riccati equation A2R−RA1 = A3+RA4R, Studia Math. 147 (2001), no. 1, 15–26.
M.T. Nair, An iterated version of Lavrentiev’s method for ill-posed equations with approximately specified data, J. Inverse Ill-Posed Probl. 8 (2000), no. 2, 193–204.
S.H. Kulkarni & M.T. Nair, A characterization of closed range operators, Indian J. Pure Appl. Math. 31 (2000), no. 4, 353–361.
M.T. Nair, On Morozov’s method for Tikhonov regularization as an optimal order yielding algorithm, Z. Anal. Anwendungen 18 (1999), no. 1, 37–46.
S. George & M.T. Nair, On a generalized Arcangeli’s method for Tikhonov regularization with inexact data, Numer. Funct. Anal. Optim. 19 (1998), no. 7-8, 773–787.
M.T. Nair, An iterated regularized approximation procedure for ill-posed operator equations, Progr. Math. (Varanasi) 32 (1998), no. 2, 51–61.
M.T. Nair & E. Schock, A discrepancy principle for Tikhonov regularization with approximately specified data, Ann. Polon. Math. 69 (1998), no. 3, 197–205.
M.T. Nair, M. Hegland & R.S. Anderssen, The trade–off between regularity and stability in Tikhonov regularization, Math. Comp. 66 (1997), no. 217, 193–206.
S. George & M.T. Nair, Error bounds and parameter choice strategies for simplified regularization in Hilbert scales, Integral Equations Operator Theory 29 (1997), no. 2, 231–242.
M.T. Nair, On spectral properties of perturbed operators, Proc. Amer. Math. Soc. 123 (1995), no. 6, 1845–1850.
B.V. Limaye & M.T. Nair, On multiplicities and ascent of an eigenvalue of a linear operator, Math. Student 64 (1995), no. 1-4, 162–166 (1996).
S. George & M.T. Nair, A class of discrepancy principles for simplified regularization of ill-posed problems, J. Austral. Math. Soc. Ser. B 36 (1994), no. 2, 242–248.
S.George & M.T. Nair, Parameter choice by discrepancy principles for ill–posed problems leading to optimal convergence rates, J. Optim. Theory Appl. 83 (1994), no. 1, 217–222.
M.T. Nair, A unified approach for regularized approximation methods for Fredholm integral equations of the first kind, Numer. Funct. Anal. Optim. 15 (1994), no. 3-4, 381–389.
S. George & M.T. Nair, An a posteriori parameter choice for simplified regularization of ill-posed problems, Integral Equations Operator Theory 16 (1993), no. 3, 392–399.
M.T. Nair, On accelerated refinement methods for operator equations of the second kind, J. Indian Math. Soc. (N.S.) 59 (1993), no. 1-4, 135–140.
M.T. Nair, On strongly stable approximations, J. Austral. Math. Soc. Ser. A 52 (1992), no. 2, 251–260.
M.T. Nair, On uniform convergence of approximation methods for operator equations of the second kind, Numer. Funct. Anal. Optim. 13 (1992), no. 1-2, 69–73.
M.T. Nair, A generalization of Arcangeli’s method for ill–posed problems leading to optimal rates, Integral Equations Operator Theory 15 (1992), no. 6, 1042–1046.
M.T. Nair & R.S.Anderssen, Superconvergence of modified projection method for integral equations of the second kind, J. Integral Equations Appl. 3 (1991), no. 2, 255–269.
B.V. Limaye & M.T. Nair, Eigenelements of perturbed operators, J. Austral. Math. Soc. Ser. A 49 (1990), no. 1, 138–148.
M.T. Nair, Computable error estimates for Newton’s iterations for refining invariant subspaces, Indian J. Pure Appl. Math. 21 (1990), no. 12, 1049–1054.
M. T. Nair, On iterative refinements for spectral sets and spectral subspaces, Numer. Funct. Anal. Optim. 10 (1989), no. 9-10, 1019–1037.
M.T. Nair, Approximation of spectral sets and spectral subspaces in Banach spaces, J. Indian Math. Soc. (N.S.) 54 (1989), no. 1-4, 187–200.
M.T. Nair, A note on Rayleigh–Schroedinger series, J. Math. Phys. Sci. 23 (1989), no. 2, 185–193.
B.V. Limaye & M.T. Nair, On the accuracy of Rayleigh–Schroedinger approximations, J. Math. Anal. Appl. 139 (1989), no. 2, 413–431.
M.T. Nair, A modified projection method for equations of the second kind – Corrigendum and Addendum, Bull. Austral. Math. Soc. 40 (1989), no. 3, 487.
B.V. Limaye & M.T. Nair, Localization of a simple eigenvalue and a corresponding eigenvector, Houston J. Math. 14 (1988), no. 1, 129–141.
M.T. Nair, A modified projection method for equations of the second kind, Bull. Austral. Math. Soc. 36 (1987), no. 3, 485–492.
M.T. Nair, Role of Hilbert scales in regularization, In: Semigroups, Algebra and Operator Theory, Ed.: P.G. Romeo, Springer India, 2015.
K.P. Deepesh, S.H. Kulkarni and M.T. Nair, Generalized inverses and approximation numbers, In: Combinatorial Matrix Theory and Generalized Inverses of Matrices, Editors: R.B. Bapat, S.J. Kirkland, M.M. Prasad and S. Putenen, Springer, 2013, Pages 143- 158.
Hui Cao and M.T. Nair, Multilevel augmentation method for parameter identification problems in PDE. In: Advances in PDE Modeling and Computation, Editor: S. Sundar, Anne Books, Pvt. Ltd., 2013, Pages 52-68.
M.T. Nair, Regularization of Fedholm integral equations of the first kind using Nystr¨om approximation, In: Computational Methods for Applied Inverse Problems, Eds.: Y. Wang, A.G. Yagola, and C. Yang, De Gruyter, 2012, Pages: 65–82.
M.T. Nair, Approximation of spectral sets and spectral subspaces, Numerical Functional Analysis, and Wavelet Analysis, Eds.: S.H. Kulkarni and M.N.N. Namboodiri, Allied Publishers Pvt, Ltd., 2003, Pages: 116–125.
M.T. Nair, On a globally convergent method for integral equations of the second kind, In: Theory of Differential Equations and Applications to Oceanography, Eds., S.G.Deo and Y.S.Prahlad, Affiliated East– West Press Pvt. Ltd., 1992, Pages 143–153.
M.T. Nair, On spectral variation under relatively bounded perturbation, In: Methods of Functional Analysis in Approximation Theory, Eds., C.A.Micchelli, D.V.Pai and B.V.Limaye, Birkhauser Verlag, ISNM, 76, 1986, Pages 389–400.
B.V. Limaye and M.T. Nair, Rayleigh–Schr¨odinger approach to iterative refinements of computed eigenelements under strong approximation, In: Methods of Functional Analysis in Approximation Theory, Eds., C.A.Micchelli, D.V.Pai and B.V.Limaye, Birkhauser Verlag, ISNM, 76, 1986, Pages 371–388.
B.V. Limaye and M.T. Nair, Localization results for eigenelements, In: Modern Analysis and Applications, Ed., H.L.Manoch, Prentice Hall of India, 1983, Pages 169–178.
M.T. Nair, An interplay between numerical and functional analysis, In: Proceedings of the National Seminar on Foundations of Mathematical Analysis Editors: T. Thrivikraman and M. Haroon, 2011, Pages: 23– 29.
M.T. Nair, On Tikhonov regularization using Hilbert scales, In: Proceedings of the XII Ramanujan Symposium on Recent Trends in Analysis, Editor: G. Balasubramanian, University of Madras Publ. 2006, Pages: 18–25. 2003, Pages: 21–35.
M.T. Nair, On Order optimality of regularization methods for ill-posed problems, In: Proceedings of the National Conference on Recent Trends in Applied Mathematics, Coimbatore, 2003, Pages: 21–35. 13
M.T. Nair, Regularization and approximation of ill-posed problems, In: Proceedings of the International Conference on Recent Trends in Mathematical Analysis, Eds.: J.K. John, T. Thrivikraman, and N.R. Mangalambal, Allied Publishers, Pvt. Ltd., 2003, Pages: 33–57.
M.T. Nair and M.P. Rajan, On improving accuracy for Arcangeli’s method for solving ill-posed problems with modeling error, In: Proceedings of the International Conference on Recent Trends in Mathematical Analysis, Eds.: J.K. John, T. Thrivikraman, and N.R. Mangalambal, Allied Publishers, Pvt. Ltd., 2003, Pages: 190–198.
M.T. Nair, On some variants of projection methods for operator equations of the second kind, In: Proc. Centre for Math. Sci.,Trivandrum, 1989, Pages 21–40.
M.T. Nair, S.V. Pereverzev, and U. Tautenhahn, Regularization in Hilbert scales under general smoothing conditions*, RICAM-Report No. 2005- 09, Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria, June 2005 2002.
M.T. Nair, E. Schock, and U. Tautenhahn, Morozov’s discrepancy principle under general source conditions*, Res. Rep., Nr.330, ISSN 0943– 8874, Universit¨at Kaiserslautern, July 2002.
M.T. Nair, Optimal order results for a class of regularization methods using unbounded operators*, Res. Rep., Nr.313, ISSN 0943–8874, Universit¨at Kaiserslautern, 1999.
M.T. Nair, Error estimates for Tikhonov regularization with unbounded regularizing operators, Res. Rep., Nr.279, ISSN 0943–8874, Universit¨at Kaiserslautern, 1996.
M.T. Nair, M.Hegland, and R.S.Anderssen, The trade–off between regularity and stabilization in Tikhonov regularization*, Res. Rep., M8–94, Australian National University, 1994.
S. George and M.T. Nair, On a generalization of Arcangel’s method for Tikhonov regularization with inexact data*, Res. Rep., CMA–MR43– 93, SMS–88–93, Australian National University, 1993.
M.T. Nair, On spectral properties of perturbed operators*, Res. Rep., CMA–MR31–93, Australian National University,1993.
M.T. Nair, Tikhonov regularization and approximation for ill–posed operator equations, Res. Rep., Nr. 237, Universit¨at Kaiserslautern, 1993.
M.T. Nair and E. Schock, Regularized approximation methods with perturbation for ill–posed operator equations*, Res. Rep., Nr. 231, Universit¨at Kaiserslautern, 1992.
B.V. Limaye and M.T. Nair, Rayleigh–Schr¨odinger approach to iterative refinements of computed enfeeblements under strong approximation, Res. Rep., CMA–R20–86, Australian National University,1989.
M.T. Nair, Computable error estimates for Newton’s iterates for refining invariant subspaces*, Res. Rep., CMA–R16–89, Australian National University,1989.
M.T. Nair, On iterative refinements for spectral sets and spectral subspaces*, Res. Rep., CMA–R11–89, Australian National University,1989.
M.T. Nair and R.S. Anderssen, Superconvergence of modified projection method for integral equations of the second kind*, Res. Rep., CMA– R57–89, Australian National University,1989.