Knizhnerman, Leonid Aronovich

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Total publications: 11
Scientific articles: 11
Presentations: 2

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Knizhnerman, Leonid Aronovich
Doctor of physico-mathematical sciences
Speciality: 01.01.07 (Computing mathematics)
Birth date: 4.08.1955
Keywords: Lanczos method, Arnoldi method, extended Krylov subspace method, rational Krylov subspace method, rational approximation, optimal grids, Markov functions, variational regularization, inverse spectral problems.
UDC: 519.644, 519.651, 517.538.52, 517.538.53, 519.612


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.

Main publications:
  1. V. L. Druskin, L. A. Knizhnerman, “Error estimates for the simple Lanczos process when computing functions of symmetric matrices and eigenvalues”, J. Comput. Math. and Mathem. Phys., 31:7 (1991), 970–983
  2. L. A. Knizhnerman, “Computation of functions of unsymmetric matrices by means of the Arnoldi method”, J. Comput. Math. and Mathem. Phys., 31:1 (1991), 5–16
  3. V. Druskin and L. Knizhnerman, “Extended Krylov subspaces: approximation of the matrix square root and related functions”, SIAM J. Matrix Anal. Appl., 19:3 (1998), 755–771
  4. V. Druskin and L. Knizhnerman, “Gaussian spectral rules for second order finite-difference schemes”, Numer. Algorithms, 25:1-4 (2000), 139–159
  5. V. Druskin, L. Knizhnerman and M. Zaslavsky, “Solution of large scale evolutionary problems using rational Krylov subspaces with optimized shifts”, SIAM J. Sci. Comp., 31:5 (2009), 3760–3780
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. M. A. Botchev, L. A. Knizhnerman, “Adaptive residual-time restarting for Krylov subspace matrix exponential evaluations”, Keldysh Institute preprints, 2019, 127, 28 pp.  mathnet
2. L. A. Knizhnerman, “Padé–Faber Approximation of Markov Functions on Real-Symmetric Compact Sets”, Mat. Zametki, 86:1 (2009),  81–94  mathnet  mathscinet  zmath  elib; Math. Notes, 86:1 (2009), 81–92  isi  scopus
3. L. A. Knizhnerman, “Gauss–Arnoldi quadrature for $\langle(zI-A)^{-1}\varphi,\varphi\rangle$ and rational Padé-type approximation for Markov-type functions”, Mat. Sb., 199:2 (2008),  27–48  mathnet  mathscinet  zmath  elib; Sb. Math., 199:2 (2008), 185–206  isi  elib  scopus
4. A. Greenbaum, V. L. Druskin, L. A. Knizhnerman, “On solving indefinite symmetric linear systems by means of the Lanczos method”, Zh. Vychisl. Mat. Mat. Fiz., 39:3 (1999),  371–377  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 39:3 (1999), 350–356
5. L. A. Knizhnerman, “The simple Lanczos procedure: Estimates of the error of the Gauss quadrature formula and their applications”, Zh. Vychisl. Mat. Mat. Fiz., 36:11 (1996),  5–19  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 36:11 (1996), 1481–1492  isi
6. L. A. Knizhnerman, “The quality of approximations to a well-isolated eigenvalue, and the arrangement of “Ritz numbers” in a simple Lanczos process”, Zh. Vychisl. Mat. Mat. Fiz., 35:10 (1995),  1459–1475  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 35:10 (1995), 1175–1187  isi
7. L. A. Knizhnerman, “Error bounds in Arnoldi's method: The case of a normal matrix”, Zh. Vychisl. Mat. Mat. Fiz., 32:9 (1992),  1347–1360  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 32:9 (1992), 1199–1211  isi
8. V. L. Druskin, L. A. Knizhnerman, “Error bounds in the simple Lanczos procedure for computing functions of symmetric matrices and eigenvalues”, Zh. Vychisl. Mat. Mat. Fiz., 31:7 (1991),  970–983  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 31:7 (1991), 20–30  isi
9. L. A. Knizhnerman, “Calculation of functions of unsymmetric matrices using Arnoldi's method”, Zh. Vychisl. Mat. Mat. Fiz., 31:1 (1991),  5–16  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 31:1 (1991), 1–9  isi
10. V. L. Druskin, L. A. Knizhnerman, “Two polynomial methods of calculating functions of symmetric matrices”, Zh. Vychisl. Mat. Mat. Fiz., 29:12 (1989),  1763–1775  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 29:6 (1989), 112–121
11. L. A. Knizhnerman, V. Z. Sokolinskii, “Some estimates of rational trigonometric sums and sums of Legendre symbols”, Uspekhi Mat. Nauk, 34:3(207) (1979),  199–200  mathnet  mathscinet  zmath; Russian Math. Surveys, 34:3 (1979), 203–204

Presentations in Math-Net.Ru
1. Review of computational mathematical projects of the Mathematical Modelling Department of the Central Geophysical Expedition
L. A. Knizhnerman
XV International Conference «Algebra, Number Theory and Discrete Geometry: modern problems and applications», dedicated to the centenary of the birth of the Doctor of Physical and Mathematical Sciences, Professor of the Moscow State University Korobov Nikolai Mikhailovich
May 31, 2018 17:20
2. On the best rational approximation of the function $z^{-1/2}$ on the union of the two segments of the real line
L. A. Knizhnerman
Seminar on Complex Analysis (Gonchar Seminar)
April 27, 2015 18:00

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