## Leonid Knizhnerman — personal site

### Brief biography

I was born on August 4, 1955 in Moscow.

In 1972 I entered the mathematical faculty of the Moscow State Pedagogical Institute (presently MPSU); I graduated from the institute in 1977 with distinction. In 1977-1980 I studied as a postgraduate student at the number theory cathedra of the same faculty. I contacted Professors M. F. Bokshtein, A. A. Bukhshtab, N. M. Korobov, L. Ya. Kulikov, V. G. Lemlein, V. I. Nechaev, D. A. Raikov.

Being a student and postgraduate, I simultaneously worked at the computational mathematics cathedra (educational and scientific student research) under control of PhD. (now D. Chem. Sci.) V. A. Kronrod.

PhD degree in the junction of specialities "algebra, logic and number theory" and "computational mathematics" (scientific advisor N. M. Korobov).

Doctor of Physical aтd Mathematical Sciences in speciality "computational mathematics" (INM of RAS, 2012; the dissertation's topic is "Error estimates for the Lanczos and Arnoldi methods in exact and computer arithmetic").

The/an author of about 25 talks at Russian and international mathematical and geophysical conferences.

A reviewer of greater than 60 mathematical and geophysical papers.

A member of SIAM, SEG and ЕАГО.

In 1980 I entered the Central Geophysical Expedition. I am (was) working jointly S. K. Asvadurov, S. N. Davydycheva, V. L. Druskin, T. F. Dyakonova, A. S. Kashik, O. M. Kosenkov, A. L. Pleshkevich, N. I. Rykhlinsky, T. V. Tamarchenko, M. D. Khusid, S. V. Shchedrina. Since 1996 till 2019 I headed the Mathematical Modelling Department of the CGE (about activity of OMM see review papers No 76 and 109 in list of papers). I was working at another department since 2019 till 2021.

I was awarded with a CGE diploma "For an outstanding creative contribition into formation and development of the JSV "Central Geophysical Expedition"" (2007). I was awarded with a CGE jubelee medal "The 50th anniversary of CGE" (2017). I was awarded with an honoured diploma of Rosgeologiya "For longstanding faultless and conscientious labour, big personal contribution to the development of the geological branch and in relation with the professional holiday "The Geologist Day"" (2017). I was awarded with the badge of the Ministry of Natural Resources and Ecology of RF "Honoured specialist in Earth interior exploration" (2017).

### Areas of scientific interest

- Algebraic number theory (in the past)
- Computational linear algebra — the Lanczos and Arnoldi methods, the extended Krylov subspace method, the rational Krylov subspace method
- Numerical solution of PDEs by means of the Spectral Lanczos/Arnoldi Decomposition Methods and other linear algebra methods
- The theory of rational approximation and its applications to constructing optimal finite difference grids for solution of PDEs
- Inverse spectral problems
- Numerical solution of ill-posed geophysical problems with the use of variational regularization

### Personal pages on scientific portals

### Contacts

E-mail: lknizhnerman *at* gmail.com