Leonid Knizhnerman; collarorators: Mikhail A. Botchev and Marcel Schweitzer The Arnoldi and Lanczos methods: residual estimates for some differential equations A talk at MMMA-2023
Mike A. Botchev, Leonid A. Knizhnerman, Eugene E. Tyrtyshnikov
A residual concept for Krylov subspace evaluation of the φ matrix function arXiv:2010.08494
A. S. Kashik, L. A. Knizhnerman, M. D. Khusid
The design change of the casing with the purpose of optimization of development of deposits of hydrocarbonsBurenie i neft', 2016, # 9, p. 56-60 (in Russian).
A. S. Kashik, L. A. Knizhnerman, O. M. Kosenkov, M. D. Khusid
Development of a package of computational mathematical programs for handling measurements of a multi-electrode laterolog tool MnBKXXIth scientific and practical conference \"New technique and technologies for geophusical investigations of boreholes\", abstracts, p. 41-53. Ufa, NPF Geofizika, 2015
M. D. Khusid, A. S. Kashik, L. A. Knizhnerman
Current situation and future prospects of electrical logging in wells, cased with metal column
Proceedings of the VIII-th Chinese-Russian symposium on Geophysics, China, Beijing, 2014, p. 45-54.
Khusid M. D., Kashik A. S., Knizhnerman L. A.
Optimizing the electrologging and electro-thermal effects in cased wells via the transformations of the column's constructionGeofizika, 2014, No 4, p. 69-73 (in Russian).
Y. Lin, A. Abubakar, T. M. Habashy, G. Pan, M. Li, V. Druskin, L. Knizhnerman
Schemes for improving efficiency of pixel-based inversion algorithms for electromagnetic logging-while-drilling measurementsSEG Technical Program Expanded Abstracts 2012: 1-5.
A. S. Kashik, L. A. Knizhnerman, A. R. Klepatsky, M. D. Khusid
Modeling electro-thermal stimulation methods of the near-wellbore area during the development of high-viscosity oil depositExposition Oil Gas, 2012, p. 68-72 (in Russian).
A. S. Kashik, L. A. Knizhnerman, M. D. Khusid
Modeling electro-thermal stimulation methods during the development of high-viscosity oil and natural bitumen depositsXIX-th Gubkin’s reading "Innovative technologies forecasting, prospecting, exploration and exploitation of hydrocarbon accumulations and priority directions of the resource base development in Russian fuel and energy sector", RSUOG, 2011, p. 79-80 (in Russian).
Yong‐Hua Chen, Dzevat Omeragic, Vladimir Druskin, Chih‐Hao Kuo, Tarek Habashy, Aria Abubakar, Leonid Knizhnerman
2.5D FD modeling of EM directional propagation tools in high‐angle and horizontal wellsSEG Technical Program Expanded Abstracts 2011: 422-426.
M. Zaslavsky, V. Druskin, S. Davydycheva, L. Knizhnerman, A. Abubakar and T. Habashy
Hybrid finite-difference integral equation solver for 3D frequency domain anisotropic electromagnetic problemsGeophysics, 2011, v. 76, No. 2, p. F123-F137.
S. I. Bilibin, A. S. Kashik, A. R. Klepatsky, L. A. Knizhnerman, M. D. Khusid
The solution of the direct problems of electrical logging as the basis of the theory of methods’ development for viscous oil’s controlled extractionroceedings of the VI-th Chinese-Russian symposium on Geophysics, Part II, China, Qingdao, 2010, p. 72-87.
L. Knizhnerman, V. Druskin and M. Zaslavsky
On optimal convergence rate of the Rational Krylov Subspace Reduction for electromagnetic problems in unbounded domainsSIAM J. Numer. Anal., 2009, v. 47, № 2, pp. 953-971.
A. Abubakar, T. M. Habashy, V. L. Druskin, L. Knizhnerman, and D. Alumbaugh
2.5D forward and inverse modeling for interpreting low-frequency electromagnetic measurementsGeophysics, 2008, v. 73, № 4, pp. F165–F177.
L. A. Knizhnerman
Gauss-Arnoldi quadrature for $ igllangle(zI-A)^{-1}varphi,,varphi igr angle$ and rational Pad'e-type approximation for Markov-type functions Math. Digest, 2008, v. 199, No. 2, pp. 27-48.
A. Abubakar, T. M. Habashy, V. Druskin, L. Knizhnerman and S. Davydycheva
A 3D parametric inversion algorithm for triaxial induction dataGeophysics, 2006, v. 71, p. 1-9.
A. Abubakar, T. M. Habashy, V. L. Druskin, D. Alumbaugh, P. Zhang, M. Wilt, H. Denaclara, E. Nichols, L. Knizhnerman
A fast and rigorous 2.5D inversion algorithm for cross‐well electromagnetic dataSEG Technical Program Expanded Abstracts 2005: 534-537.
A. S. Kashik, N. I. Rykhlinsky, L. A. Knizhnerman, R. I. Krivonosov, A. S. Stepanov
On the electrical logging of boreholes, cased with steel tubes, by cable apparatusKarotazhnik, 2004, issues 3-4 (116-117), pp. 8-23 (in Russian).
Aria Abubakar, Tarek M. Habashy, Vladimir Druskin, Sofia Davydycheva, Hanming Wang, Tom Barber, Leonid Knizhnerman
A three‐dimensional parametric inversion of multi‐component multi‐spacing induction logging dataSEG Technical Program Expanded Abstracts 2004: 616-619.
S. Asvadurov, L. Knizhnerman and J. Pabon
Finite-difference modeling of viscoelastic materials with quality factors of arbitrary magnitudeGeophysics, 2004, v. 69, № 3, pp. 817-824.
S. Asvadurov, V. Druskin and L. Knizhnerman
Application of the difference Gaussian rules to solution of hyperbolic problems. II. Global expansionJ. Comput. Phys., 2002, v. 175, № 1, pp. 24-49.
S. Asvadurov, L. Knizhnerman and J. Pabon
Finite-difference modeling of viscoelastic materials with quality factors Q of arbitrary magnitudeSchlumberger-Doll Research, TR OFSR/RN/2001/151/RTMI/C.
C. Torres-Verdin, V. L. Druskin, Sheng Fang, L. A. Knizhnerman and A. Malinverno
A dual-grid nonlinear inversion technique with applications to the interpretation of dc resistivity dataGeophysics, 2000, v. 65, № 6, pp. 1733-1745.
V. Druskin and L. Knizhnerman
Gaussian spectral rules for the three-point second differences: I. A two-point positive definite problem in a semi-infinite domainSIAM J. Numer. Anal., 1999, v. 37, № 2, pp. 403-422.
V. L. Druskin, L. A. Knizhnerman and Ping Lee
New spectral Lanczos decomposition method for induction modeling in arbitrary 3-D geometryGeophysics, 1999, v. 64, № 3, pp. 701-706.
B. Anderson, T. Barber, V. Druskin, Ping Lee, E. Dussun, L. Knizhnerman and S. Davydycheva
The response of multiarray induction tools in highly dipping formations with invasion and in arbitrary 3D geometries
The Log Analist, 1999, v. 40, № 5, pp. 327-344.
B. I. Anderson, V. Druskin, Ping Lee, M. G. Luling, E. Schoen, J. Tabanou, P. Wu, S. Davydycheva, and L. Knizhnerman
Modeling 3-D effects on 2-MHz LWD resistivity logs
In: Transactions of the SPWLA (Society of Professional Well Log Analysts) Thirty-Eighth Annual Logging Symposium, June 15-18, 1997: Houston, Tex., Society of Professional Well Log Analysts, Paper N, 14 p.
V. Druskin, L. Knizhnerman, S. Kostek and T. Tamarchenko
Krylov subspace reduction and its extensions for option pricing
Comput. Finance, 1997, v. 1, № 1.
L. Knizhnerman
On adaptation of the Arnoldi method to the spectrumSchlumberger-Doll Research, Res. Note #EMG-001-96-03, February 12, 1996.
V. Druskin and L. Knizhnerman
Exponential split preconditioning of Krylov subspaces to compute functions of elliptic operators, illustrated by the 3-D diffusion and Maxwell equationsSchlumberger-Doll Research, Rep. № EMG-001-95-23, November 29, 1995.
M. van der Horst, V. Druskin, L. Knizhnerman
Modelling the response of induction logging tools in 3D geometries with the Spectral Lanczos Decomposition Method
Schlumberger-Doll Research, Res. Note #EMG-001-95-18, September 18, 1995.
L. Knizhnerman
On adaptation of the Lanczos method to the spectrum
Schlumberger-Doll Research, Res. Note #EMG-001-95-12, May 12, 1995.
Vladimir Druskin, Leonid Knizhnerman
An efficient new method for solving large‐scale electromagnetic problems in inhomogeneous conductive media in the time and frequency domains
SEG Technical Program Expanded Abstracts 1993: 358-359.
A. Hordt, V. Druskin, L. Knizhnerman, and K.-M. Strack
Interpretation of 3-D effects in deep transient electromagnetic (LOTEM) soundings in the Münsterland area (Germany)
Geophysics, 1992, v. 57, № 9, pp. 1127-1137.
V. Druskin and L. Knizhnerman
Evaluations for Krylov subspace approximation to internal eigenvalues of large symmetric matrices and bounded self-adjoint operators with continuous spectrum
Schlumberger-Doll Research, Res. Note, September 2, 1992.
A. S. Kashik, L. A. Knizhnerman
On stabilization of the statements of geophysical inverse problems
Geology and Geophysics, 1989, No. 1, pp. 126-129. (In Russian; translated into English)
L. A. Knizhnerman
A numerical method of continuation of potential fields from a bounded region of the Earth surface
Izv. AN USSR, ser. "Physics of Solid Earth", 1988, No. 12, pp. 23-30. (In Russian; translated into English)
V. L. Druskin, L. A. Knizhnerman
A spectral semi-discrete method for the numerical solution of three-dimensional non-stationary electrical prospecting problems
Izv. AN USSR, ser. "Physics of Solid Earth", 1988, No. 8, pp. 63-74. (In Russian; translated into English)
L. A. Knizhnerman
On applications of the optimal coefficients method to the numerical solution of some problems of mathematical physics
Saratov Univ., "Investigations on number theory", 1988, pp. 32-38. (In Russian)
V. L. Druskin, L. A. Knizhnerman
On an iterative algorithm for the solution of a two-dimensional inverse electrical logging problem
Geology and Geophysics, 1987, No. 9, pp. 118-123. (In Russian; translated into English)
L. A. Knizhnerman, V. Z. Sokolinsky
On exponential sums and sums of the Legendre symbol with large and small absolute values
Saratov Univ., "Investigations on number theory", 1987, pp. 76-89. (In Russian)
V. L. Druskin, L. A. Knizhnerman
A method for the solution of direct problems of electrical logging and electrical prospecting with direct current
Izv. AN USSR, ser. "Physics of Solid Earth", 1987, No. 4, pp. 63-71. (In Russian; translated into English)
V. L. Druskin, L. A. Knizhnerman
The use of operator series in orthogonal polynomials when computing functions of self-adjoint operators and the justification of the Lanczos phenomenon
Moscow, IZMIR AN USSR, dep. at VINITI 02.03.1987, No. 1535-B27, 47 p. (In Russian)
V. L. Druskin, A. S. Kashik, L. A. Knizhnerman, O. M. Kosenkov
The solution of an inverse electrical logging problem for axial symmetric inhomogeneous models
"Mathem. methods of identification in geological problems", Moscow, Nauka, 1985, pp. 109-116. (In Russian)
L. A. Knizhnerman
The effectiveness of recognition as a way of choosing a regularization parameter when analytically continuing potential fields by decomposing into Chebyshev series
Izv. AN USSR, ser. "Physics of Solid Earth", 1985, No. 5, pp. 87-90. (In Russian)
L. A. Knizhnerman
Extraction of poles of potential fields by means of decomposition into Fourier-Chebyshev series
Izv. AN USSR, ser. "Physics of Solid Earth", 1984, No. 11, pp. 119-123. (In Russian; translated into English)
L. A. Knizhnerman
The numerical solution of Cauchy's problem for the Laplace equation by means of decomposition into Fourier-Chebyshev series
Izv. AN USSR, ser. "Physics of Solid Earth", 1984, No. 10, pp. 76-81. (In Russian; translated into English)
V. A. Milashin, L. A. Knizhnerman
A first attempt of optimization of schemes of field measurements by means of a computer
VNIIOENG, "Oil and Gas Geology, Geophysics and Drilling", 1984, issue 8, pp. 24-26. (In Russian)
L. A. Knizhnerman
An error estimate for a nonlinear variational regularization method of determining poles of potential fields
Ed. Board of the J. "Izv. Vuzov", ser. "Geol. and Prosp.", dep. at VINITI 09.09.1983, No. 5173-83 Dep., 15 pp. (In Russian)
L. A. Knizhnerman
An adaptive variational regularization method of soving Cauchy's problem for a two-dimensional Laplace equation
Ed. Board of the J. "Izv. Vuzov", ser. "Geol. and Prosp.", dep. at VINITI 09.09.1983, No. 5170-83 Dep., 8 pp. (In Russian)
V. L. Druskin, L. A. Knizhnerman
On determination of the first boundary in a two-dimensional inverse problem of electrical prospecting
Nauka, "Math. methods of identification of models in Geology", 1983, pp. 126-134. (In Russian)
L. A. Knizhnerman, V. A. Kronrod, V. Z. Sokolinsky, V. V. Shchennikov
On the numerical solution of a three-dimensional nonlinear Poisson equation
Syb. Energ. Inst., "Numerical methods of Analysis", 1980, pp. 89-93. (In Russian)
L. A. Knizhnerman
A number-theoretical method of solving Cauchy's problem for Poisson's equation
MSPI, dep. at VINITI 21.04.1980, No. 1568-80 Dep., 22 pp. (In Russian)
L. A. Knizhnerman
A number-theoretical method of solving some problems for partial differential equations
MSPI, dep. at VINITI 26.02.1980, No. 712-80 Dep., 24 pp. (In Russian)
L. A. Knizhnerman, V. Z. Sokolinsky
On unimprovability of A. Weil's estimates for rational exponential sums and sums of the Legendre symbol
MSPI, dep. at VINITI 29.05.1979, No. 2152-79 Dep., 15 pp. (In Russian)
L. A. Knizhnerman, V. A. Kronrod, V. Z. Sokolinsky
A numerical method to solve Poisson's equation with an enhanced order of accuracy
MSPI, "Comput. Math. and Progr.", 1978, issue 7, pp. 12-14. (In Russian)
V. A. Kronrod, L. A. Knizhnerman, V. Z. Sokolinsky
Some numerical experiments on solving Poisson's equation by means of a fast converging economical method
MSPI, "Comput. Math. and Progr.", 1978, issue 6, pp. 130-135. (In Russian)