Demyanko
K. V., Kaporin I. E., Nechepurenko Y. M. Inexact Newton
method for the solution of eigenproblems arising in
hydrodynamic temporal stability analysis // Journal of
Numerical Mathematics. 2020. V. 28. No. 1. P. 1-14.
DOI: https://doi.org/10.1515/jnma-2019-0021
Kaporin I. Preconditioned Subspace Descent Method for
Nonlinear Systems of Equations //Open Computer Science.
2020. V. 10. No. 1. P. 71-81.
DOI: https://doi.org/10.1515/comp-2020-0012
Kaporin I., Milyukova O. MPI+OpenMP Implementation of the
BiCGStab Method With Explicit Preconditioning for the
Numerical Solution of Sparse Linear Systems // Numerical
methods and programming. 2020. V.20. No.4. P.516-527.
DOI: https://doi.org/10.26089/NumMet.v20r445
Golikov, A. I., Yu G. Evtushenko, and I. E. Kaporin.
Newton-Type Method for Solving Systems of Linear Equations and
Inequalities// Computational Mathematics and Mathematical
Physics. 2019. V. 59, no. 12. P.2017-2032.
DOI: https://doi.org/10.1134/S0965542519120091
Golikov A.I., Kaporin I.E. Inexact Newton method for
minimization of convex piecewise quadratic functions. In:
Numerical Geometry, Grid Generation and Scientific Computing
2019 (P. 139-155). Springer, Cham.
DOI: https://doi.org/10.1007/978-3-030-23436-2_10
https://arxiv.org/pdf/1901.03245.pdf
Kaporin I. Using Sparse Principal Component Methods for
Approximating Restricted Isometry Constants of Complex-Valued
Tight Frames // Proc. IX International Conference on
Optimization and Applications (OPTIMA 2018) (Supplementary
Volume) , P. 297-310.
DOI: https://doi.org/10.12783/dtcse/optim2018/27941
Kaporin I. E. Bounding the restricted isometry constants for a
tight frame //Sbornik: Mathematics. 2017. V. 208. No. 11. P.
1646-1660.
DOI: https://doi.org/10.1070/SM8822
Konshin, I., Kaporin, I., Nikitin, K., Vassilevski, Y. Parallel linear systems solution for multiphase flow problems in the INMOST framework. Proceedings of the 1st Russian Conference on Supercomputing - Supercomputing Days 2015, Moscow, Russia, September 28-29, 2015 (pp. 96-103). Kaporin, I. E. E., Milyukova, O. Y. (2013). Optimization of the factorized preconditioners of conjugate gradient method for solving the linear algebraic systems with symmetric positive definite matrix. Preprints of the Keldysh Institute of Applied Mathematics, 13-17. Kaporin, I. E. E. (2012). Using Chebyshev polynomials and approximate inverse triangular factorizations for preconditioning the conjugate gradient method. Computational Mathematics and Mathematical Physics, 52(2), 169-193. Kaporin, I. (2010). Scaling, preconditioning, and superlinear convergence in GMRES-type iterations. In Matrix Methods: Theory, Algorithms And Applications: Dedicated to the Memory of Gene Golub (pp. 273-295). Kaporin, I., Konshin, I. (2009). Load Balancing of Parallel Block Overlapped Incomplete Cholesky Preconditioning. In Parallel Computing Technologies (pp. 304-315). Springer Berlin Heidelberg. Kaporin, I. E., Kon’shin, I. N. (2009). Post-filtering of IC2-factors for load balancing in parallel preconditioning. Computational Mathematics and Mathematical Physics, 49(6), 901-918. Kaporin, I. (2008). Multilevel ILU preconditionings for general unsymmetric matrices. In Proc. Int. Conf. NUMGRID/VORONOI-2008, Moscow (pp. 150-157). Kaporin, I. E. (2008). Localization of the eigenvalues of a pencil of positive definite matrices. Computational Mathematics and Mathematical Physics, 48(11), 1917-1926. Kaporin, I. E. (2007). Scaling, reordering, and diagonal pivoting in ILU preconditionings. Russian Journal of Numerical Analysis and Mathematical Modelling rnam, 22(4), 341-375. Kaporin, I. (2005). Superlinear convergence in minimum residual iterations. Numerical linear algebra with applications, 12(5-6), 453-470. Garanzha, V. A., Kaporin, I. E. (2005). On the convergence of a gradient method for the minimization of functionals in finite deformation elasticity theory and for the minimization of barrier grid functionals. Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 45(8), 1450-1465. Kaporin, I. (2004). The aggregation and cancellation techniques as a practical tool for faster matrix multiplication. Theoretical Computer Science, 315(2), 469-510. Garanzha, V., Kaporin, I., Konshin, I. (2004). Truncated Newton type solver with application to grid untangling problem. Numerical Linear Algebra with Applications, 11(5-6), 525-533. Kaporin, I. E. E. (2003). Applications of the internal iterations of the conjugate gradients method to solution large scale sparse non-linear optimization problems. Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 43(6), 802-807. Kaporin, I. E. (2003). Using inner conjugate gradient iterations in solving large-scale sparse nonlinear optimization problems. Computational mathematics and mathematical physics, 43(6), 766-771. Kaporin, I. E. (2002). Using the modified 2nd order incomplete Cholesky decomposition as the conjugate gradient preconditioning. Numerical linear algebra with applications, 9(6-7), 401-408. Kaporin, I. E., Konshin, I. N. (2002). A parallel block overlap preconditioning with inexact submatrix inversion for linear elasticity problems. Numerical linear algebra with applications, 9(2), 141-162. Axelsson, O., Kaporin, I. (2001). Error norm estimation and stopping criteria in preconditioned conjugate gradient iterations. Numerical Linear Algebra with Applications, 8(4), 265-286. Kaporin, I. E., Kon'shin, I. N. (2001). Parallel solution of symmetric positive definite systems based on decomposition into overlapping blocks. Computational mathematics and mathematical physics, 41(4), 481-493. Axelsson, O., Kaporin, I. (2001). Optimizing two-level preconditionings for the conjugate gradient method (pp. 3-21). Springer Berlin Heidelberg. Axelsson, O., Kaporin, I. (2000). On the sublinear and superlinear rate of convergence of conjugate gradient methods. Numerical Algorithms, 25(1-4), 1-22. Axelsson, O., Kaporin, I., Konshin, I., Kucherov, A., Neytcheva, M., Polman, B., Yeremin, A. (2000). Comparison of algebraic solution methods on a set of benchmark problems in linear elasticity. Final Report of the STW project NNS, 4683. Yeremin, A. Y., Kaporin, I. E. (2000). The influence of isolated largest eigenvalues on the numerical convergence of the CG method. Journal of Mathematical Sciences, 101(4), 3231-3236. Axelsson, O., Kaporin, I. (2000). A survey of Newton type methods for solving nonlinear boundary value problems. Hellenic European Research on Mathematics and Informatics Science, HERMIS–\mu\pi, 1, 93-108. Garanzha, V. A., Kaporin, I. E. (1999). Regularization of the barrier variational method of grid generation. Computational mathematics and mathematical physics, 39(9), 1426-1440. Kaporin, I. E., Konshin, I. N. (1999). Parallel solution of large sparse SPD linear systems based on overlapping domain decomposition. In Parallel Computing Technologies (pp. 436-446). Springer Berlin Heidelberg. Kaporin, I. E. (1998). High quality preconditioning of a general symmetric positive definite matrix based on its UTU+UTR+RTU-decomposition. Numerical linear algebra with applications, 5(6), 483-509. Garanzha, V. A., Kaporin, I. E., Konshin, V. N. (1998). Reliable flow solver based on the high order control volume Pade-type differences. In Sixteenth International Conference on Numerical Methods in Fluid Dynamics (pp. 278-283). Springer Berlin Heidelberg. Kaporin, I. E., Axelsson, O. (1995). On a class of nonlinear equation solvers based on the residual norm reduction over a sequence of affine subspaces. SIAM Journal on Scientific Computing, 16(1), 228-249. Axelsson, O., Kaporin, I. E. (1995). On the solution of nonlinear equations for nondifferentiable mappings (pp. 38-51). Vieweg+Teubner Verlag. Kaporin, I. E. (1994). New convergence results and preconditioning strategies for the conjugate gradient method. Numerical linear algebra with applications, 1(2), 179-210. Kaporin, I. E. (1994). Optimization of conjugate gradient algorithms. Computational Mathematics and Modeling, 5(2), 139-147. Gushchin, I. S., Kaporin, I. E. (1994). Application of direct methods to solve difference problems of gas-discharge physics. Computational Mathematics and Modeling, 5(2), 120-126. Kaporin, I. (1993). Spectrum boundary estimation for two-side explicit preconditioning. Vestnik Mosk. Univ., ser.Math., 15, 28-42. Kaporin, I. E. (1993). Iterative solution of systems of linear equations using incomplete inverse triangular factorization. Computational Mathematics and Modeling, 4(1), 28-32. Kaporin, I. E. (1992). Explicitly preconditioned conjugate gradient method for the solution of unsymmetric linear systems. International journal of computer mathematics, 44(1-4), 169-187. Kaporin, I. E. (1992). Two-level explicit preconditioning of conjugate gradient method. Differential Equations, 28(2), 280-289. Kaporin, I. E., Kolotilina, L. Y., Yeremin, A. Y. (1991). Block SSOR preconditionings for high-order 3D FE systems. II. Incomplete BSSOR preconditionings. Linear algebra and its applications, 154-156, 647-674. Kaporin, I. E. (1991). Minimal iteration methods utilizing the generalized Krylov basis. Computational Mathematics and Modeling, 2(1), 10-16. Kaporin, I. E. (1990). A preconditioned conjugate-gradient method for solving discrete analogs of differential problems. Differential Equations, 26(7), 897-906. Kaporin, I. E. (1990). An alternative approach to estimating the convergence rate of the CG method. Numerical Methods and Software, Yu. A. Kuznetsov, ed., Dept. of Numerical Mathematics, USSR Academy of Sciences, Moscow, 55-72. Yeremin, A. Y., Kaporin, I. E. E., & Kerimov, M. K. (1988). Computation of the derivatives of the Riemann zeta-function in the complex domain. USSR Computational Mathematics and Mathematical Physics, 28(4), 115-124. Eremin, A. Y., Kaporin, I. E. (1987). Spectral optimization of explicit iterative methods. I. Journal of Soviet Mathematics, 36(2), 207-214. Gasanov, A. I., Kaporin, I. E. (1986). Application of the elimination method in the solution of strongly elliptic systems by the finite element method. Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 26(6), 837-850. Eremin, A. Y., Kaporin, I. E., Kerimov, M. K. (1985). The calculation of the Riemann zeta-function in the complex domain. USSR Computational Mathematics and Mathematical Physics, 25(2), 111-119. Yeremin, A. Y., Kaporin, I. E., Kerimov, M. K. (1985). Calculation of the Riemann zeta function in a complex domain. Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 25(4), 500-511. Yeremin, A. Y., Kaporin, I. E. (1984). Spectral optimization of explicit iterative methods. I. Chislennye Metody i Voprosy Organizatsii Vychislenii 7. Zapiski Nauchnykh Seminarov POMI, 139, 51-60. Samarskii, A. A., Kaporin, I. E., Kucherov, A. B., Nikolaev, E. S. (1983). Some modern methods of solution of difference equations. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, (7), 3-12. Kaporin, I. E., Nikolaev, E. S. (1983). Artificial unknown conjugate-direction method for finite difference elliptic problems with variable coefficients. Differential Equat., 18(7), 842-846. Kaporin, I., Nikolaev, E. (1982). Complete reduction method for a set of special 3-point vector equations. Doklady Akademii Nauk SSSR, 264(5), 1056-1059. Kaporin, I. E. (1982). A marching method for system with a block-tridiagonal matrix. In Numerical Methods of Linear Algebra (pp. 63-72). Izd. MGU Moscow. Kaporin, I. E. (1980). Modified Marching Algorithm for Solving Difference Equations Approximating Dirichlet Problem for Poisson Equation in a Rectangular. In Difference Methods for Mathematical Physics Problems (p. 11). Kaporin, I. E. (1980). A new fast Fourier transform algorithm. USSR Computational Mathematics and Mathematical Physics, 20(4), 253-259. Kaporin, I. E., Nikolaev, E. S. (1980). The method of fictitious unknowns for solving difference elliptic equations in irregular domains. Differents. Uravn., 16(7), 1211-1225. Kaporin, I. E., Nikolaev, E. S. (1980). Fictitious-Variable Method for the Solution of Elliptic Finite-Difference Boundary-Value Problems in Irregular Regions. Differential Equat., 16(7), 756-767. Kaporin, I. E., Nikolaev, E. S. (1980). The method of fictitious unknowns for solving equations of elliptic type in domains of complex shape. In Dokl. Akad. Nauk SSSR (Vol. 251, No. 3, pp. 544-548).