Publications 

Mathematical Reviews: Papers & Books (MATHSCINET); ‪Google Scholar‬ 

A Volume in honour of M. Thamban Nair (Springer: Book © 2025):

• Inverse Problems, Regularization Methods and Related Topics, 

New Book!

• Well-Posed and Ill-Posed Equations: Approximation and Regularization, World Scientific, 2026.               https://doi.org/10.1142/14440 | March 2026

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Books 

• Well-Posed and Ill-Posed Equations: Approximation and Regularization, World Scientific, 2026, 

https://doi.org/10.1142/14440 | March 2026

• Calculus of One Variable, Ane Books Pvt.,New Delhi, Second Edition 2021; Also by Springer, 2022.

• Functional Analysis: A First Course , PHI learning, Second edition 2021.

• Measure and Integration: A First Course, Taylor & Francis, CRC Press, 2019. (See: Review by MAA)

• Linear Algebra (co-author A. Singh), Springer, 2018. (See Review by MAA)

• Calculus of One Variable, Ane Books Pvt. Ltd., New Delhi, 2014

• Functional Analysis, NPTEL Web Course, IIT Madras, 2012.

• Linear Operator Equations: Approximation and Regularization, World Scientific, 2009. (See AMS Review) 

• Functional Analysis: A First Course , Prentice-Hall of India, New Delhi, 2002 (Fourth print: 2014).

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Research papers:

In refereed national and international journals 

1.   S. Mondal & M.T. Nair,  Convergence rates for a source identification problem with time-integral observation, Applicable Analysis, 2025, VOL. 104, NO. 7, 1205–1224 ( https://doi.org/10.1080/00036811.2024.2426221)

2. S. Mondal & M.T. Nair,  A source identification problem in a bi-parabolic equation: convergence rates and some optimal results,  Numer. Funct. Anal. Optim. Volume 45, 2024 - Issue 3, 27 Pages; https://doi.org/10.1080/01630563.2024.2318586

3. M.T. Nair and P. Danumjaya,  A new regularization for a time-fractional backward heat conduction problem, J. Inverse Ill-Posed Probl. Vol. 32, Issue 1, 2023, Published online by De Gruyter June 27, 2023;  arXiv:2303.15455 [math.NA]

4. A. Yadav, A. Setia and M. T. Nair,  Error Analysis for a residual based Galerkin method for a system of Cauchy singular equations with vanishing end-point conditions,  Journal of Computational and Applied Mathematics,  Volume 436, 15 January 2024, 115365. Availbale online, 27 May 2023, 115365. 

5. M. T. Nair and B. Pradeep,  Interpolation inequalities for modified Sobolev spaces and their implications to inversion of Radon transform, Proceedings of the Indian National Science Academy, Volume 89, issue 2, June 2023; https://doi.org/10.1007/s43538-023-00164-y

6. M.T. Nair & S.D. Roy, A new regularization method for a parameter identification problem in a non-linear partial differential equation, J. Part. Diff. Eq., Vol. 36. No.2. (2023) pp. 147-190. https://doi.org/10.48550/arXiv.2002.09848, February 2020.

7. M.T. Nair, An iterative approximation of $\pi$, At Right Angles, Azim Premji University At Right Angles, November 2022

8. 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. 

9. P. Mathe, M.T. Nair & B. Hofmann, Regularization of linear ill-posed problems involving multiplication operators,  Appl. Anal. 101 (2022), no. 2, 714–732.

10. M.T. Nair, Regularization of ill-posed operator equations: An overview,  J. Anal. 29 (2021), no. 2,519–541. 

11. 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

12. 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

13. 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. 

14. 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

15. 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

16. 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

17. 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. 

18. 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

19. M.T. Nair, A discrete regularization method for Ill-posed operator equations,  J. Anal. 25 (2017), no. 2, 253–266. 

20. 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

21. 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

22. 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

23. M.T. Nair, Compact operators and Hilbert scales in ill-posed problems, Math. Student 85 (2016), no. 1-2, 45–61. 

24. 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.

25. 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.

26. 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

27. 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.

28. 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

29. 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

30. 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

31. 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

32. P. Mahale & M.T. Nair, Iterated Lavrentive regularization for nonlinear ill-posed problems, ANZIAM J. 51 (2009), no. 2, 191–217.  

33. 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.

34. P. Mahale & M.T. Nair, Simplified generalized Gauss Newton method for nonlinear ill-posed problems,  Math. Comp. 78 (2009), no. 265, 171–184.

35. 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

36. M.T. Nair, On regularization of compact operator equations,   J. Anal. 16 (2008), 67–80. 

37. 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.

38. M.T. Nair & U. Tautenhahn, Convergence rates for Lavrentievtype regularization in Hilbert scales,  Comput. Methods Appl. Math. 8 (2008), no. 3, 279–293.

39. 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.

40. 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.

41. 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.

42. 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.

43. 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. 

44. 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.

45. M.T. Nair, On improving error estimates for Tikhonov regularization using an unbounded operator,  J. Anal. 14 (2006), 143–157. 

46. M.T. Nair, S. Perverziev & U. Tautenhahn, Regularization in Hilbert scales for under general smoothing conditions,  Inverse Problems 21 (2005), no. 6, 1851–1869. 

47. M.T. Nair, Eigenpairs of perturbed matrices,  J. Anal. 12 (2004), 171–181. 

48. M.T. Nair & Shinelal, Finite dimensional realization of mollifier method for compact operator equations,  Math. Comp. 74 (2005), no. 251, 1281–1290.

49. 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. 

50. M.T. Nair & U. Tautenhahn, Lavrentiev’s regularization under general source conditions,  Z. Anal. Anwendungen 23 (2004), no. 1, 167–185.

51. 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. 

52. 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. 

53. M.T. Nair, E. Schock & U.Tautenhahn, Morozov’s discrepancy principle under general source conditions,   Z. Anal. Anwendungen 22 (2003), no. 1, 199–214.

54. 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.

55. 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. 

56. M.T. Nair, Multiplicities of an eigenvalue: Some observations, Resonance, (12) (2002)  31–41. 

57. 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. 

58. 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.

59. 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.

60. 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.

61. M.T. Nair, An iterative procedure for solving Riccati equation A2R−RA1 = A3+RA4R, Studia Math. 147 (2001), no. 1, 15–26. 

62. 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.

63. S.H. Kulkarni & M.T. Nair, A characterization of closed range operators,  Indian J. Pure Appl. Math. 31 (2000), no. 4, 353–361. 

64. 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. 

65. 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.

66. M.T. Nair, An iterated regularized approximation procedure for ill-posed operator equations,  Progr. Math. (Varanasi) 32 (1998), no. 2, 51–61. 

67. M.T. Nair & E. Schock, A discrepancy principle for Tikhonov regularization with approximately specified data,   Ann. Polon. Math. 69 (1998), no. 3, 197–205. 

68. 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. 

69. 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. 

70. M.T. Nair, On spectral properties of perturbed operators,  Proc. Amer. Math. Soc. 123 (1995), no. 6, 1845–1850. 

71. 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). 

72. 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.

73. 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. 

74. 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.

75. 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.

76. 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. 

77. M.T. Nair, On strongly stable approximations,  J. Austral. Math. Soc. Ser. A 52 (1992), no. 2, 251–260. 

78. 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.

79. 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.

80. 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. 

81. B.V. Limaye & M.T. Nair, Eigenelements of perturbed operators,  J. Austral. Math. Soc. Ser. A 49 (1990), no. 1, 138–148. 

82. 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.

83. M. T. Nair, On iterative refinements for spectral sets and spectral subspaces,  Numer. Funct. Anal. Optim. 10 (1989), no. 9-10, 1019–1037.

84. 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. 

85. M.T. Nair, A note on Rayleigh–Schroedinger series, J. Math. Phys. Sci. 23 (1989), no. 2, 185–193. 

86. B.V. Limaye & M.T. Nair, On the accuracy of Rayleigh–Schroedinger approximations,   J. Math. Anal. Appl. 139 (1989), no. 2, 413–431. 

87. 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. 

88. B.V. Limaye & M.T. Nair, Localization of a simple eigenvalue and a corresponding eigenvector, Houston J. Math. 14 (1988), no. 1, 129–141. 

89. M.T. Nair, A modified projection method for equations of the second kind, Bull. Austral. Math. Soc. 36 (1987), no. 3, 485–492.

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In RMS-News letters

90.   M.T. Nair, On some isometries on ceertain function spaces,  Math. Newsl. 34 (2023), no. 1 &2, 3 pages. 

91.      On Some Isometries on Certain Function Spaces

92. M.T. Nair, A note on compactness of closed unit ball in a normed linear space. Math. Newsl. 27 (2016), no. 2, 168–170.

93. S. Kesavan and M.T. Nair,  A note on some approximation theorems in measure theory, Math. Newsl. 27 (2016), no. 2, 170–174.

94. M.T. Nair, Backward heat conduction problem, Math. Newsl. 22 (2012) 231- 239.

95. M.T. Nair, Least-square solution and regularization of matrix equations, Math. Newsl. 19 (2009) 37-44.

96. M.T. Nair, Importance of some important theorems in functional analysis, Math. Newsl. 16  (2006), no. 2, 29-32.

In math.arXive (Not in Journals)

1. V. Alavani, P. Danumjaya, and M.T. Nair,  A regularization for time-fractional backward heat conduction problem with inhomogeneous source function,  arXiv:2405.18074v, https://doi.org/10.48550/arXiv.2405.18074

2. L. Grammont & M.T. Nair, A projection based regularized approximation metnod for ill-posed operator equations,  HAL Id: hal-01782310 https://hal.archives-ouvertes.fr/hal-01782310, May 1, 2018.

Book Chapters

1. M.T. Nair (2025),  Some Regularized Approximation Methods for Ill-Posed Operator Equations. In: Pereverzyev, S.V., Radha, R., Sivananthan, S. (eds) Inverse Problems, Regularization Methods and Related Topics. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-97-7989-5_7, 2025.

2. Grammont, L., Nair, M.T., Vasconcelos, P.B. (2025). Projection-Based Approximations of Integral Equation of the First Kind. In: Pereverzyev, S.V., Radha, R., Sivananthan, S. (eds) Inverse Problems, Regularization Methods and Related Topics. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-97-7989-5_2

3. M.T. Nair (2015),  Role of Hilbert scales in regularization, In: Semigroups, Algebra and Operator Theory, Ed.: P.G. Romeo, Springer India.

4. K.P. Deepesh, S.H. Kulkarni and M.T. Nair (2013), 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, Pages 143- 158.

5. Hui Cao and M.T. Nair (2013),  Multilevel augmentation method for parameter identification problems in PDE. In: Advances in PDE Modeling and Computation, Editor: S. Sundar, Anne Books, Pvt. Ltd., Pages 52-68. 

6. M.T. Nair (2012) 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, Pages: 65–82. 

7. M.T. Nair (2003) 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., Pages: 116–125.

8. M.T. Nair (1992), 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., Pages 143–153. 

9. M.T. Nair (1986),  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, Pages 389–400.

10. B.V. Limaye and M.T. Nair (1986), 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, Pages 371–388. 

11. B.V. Limaye and M.T. Nair (1983), Localization results for eigenelements, In: Modern Analysis and Applications, Ed., H.L.Manoch, Prentice Hall of India, Pages 169–178. 

In Proceedings of conferences

1. 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. 

2. 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. 

3. 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 

4. 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. 

5. 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. 

6. 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. 

As  Research Reports of ANU, Univ. Kasiserslautern & RICAM

1. 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.

2. 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. 

3. 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. 

4. M.T. Nair, Error estimates for Tikhonov regularization with unbounded regularizing operators, Res. Rep., Nr.279, ISSN 0943–8874, Universit¨at Kaiserslautern, 1996. 

5. 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. 

6. 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. 

7. M.T. Nair, On spectral properties of perturbed operators*, Res. Rep., CMA–MR31–93, Australian National University,1993. 

8. M.T. Nair, Tikhonov regularization and approximation for ill–posed operator equations, Res. Rep., Nr. 237, Universit¨at Kaiserslautern, 1993. 

9. M.T. Nair and E. Schock, Regularized approximation methods with perturbation for ill–posed operator equations*, Res. Rep., Nr. 231, Universit¨at Kaiserslautern, 1992. 

10. 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. 

11. M.T. Nair, Computable error estimates for Newton’s iterates for refining invariant subspaces*, Res. Rep., CMA–R16–89, Australian National University,1989. 

12. M.T. Nair, On iterative refinements for spectral sets and spectral subspaces*, Res. Rep., CMA–R11–89, Australian National University,1989. 

13. 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. 

(*) Modified forms of these reports appeared as publications in refereed journals. 

In Souvenir of Forays, IIT Madras

1. On equivalence of CGT, BIT and UBP, Forays-2017.

2. Invertibility of linear operators, Forays-2015. 

3. Is there a focus for a concave spherical mirror? Forays-2014 

4. An interplay between numerical and functional analysis, Forays-2013 

5. Least-square solution of matrix equations, Forays-2010. 

6. Completeness sans Cauchy, Forays-2005 

7. Multiplicities of an eigenvalue: Some observations, Forays-2000 

8. On Caratheodary’s characterization of differentiability, Forays-1998 

9. INFINITY – The miraculous object of mathematics, Forays-1997