C. Karner, V. Kazeev and P. C. Petersen. Limitations of neural network training due to numerical instability of backpropagation. Advances in Computational Mathematics , 2024, Vol. 50, Art.14. DOI: 10.1007/s10444-024-10106-x.
V. Kazeev, I. Oseledets, M. Rakhuba and Ch. Schwab. Quantized tensor FEM for multiscale problems: diffusion problems in two and three dimensions. Multiscale Modeling & Simulation, 2022, Vol.. 3, P. 893–935. DOI: 10.1137/20M1341659.
M. Bachmayr and V. Kazeev. Stability of low-rank tensor representations and structured multilevel preconditioning for elliptic PDEs. Foundations of Computational Mathematics, 2020, Vol. 20, P.1175–1236. DOI: 10.1007/s10208-020-09446-z.
V. Kazeev and Ch. Schwab. Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions. Numerische Mathematik, 2018, Vol. 138, P. 133–190. DOI: 10.1007/s00211-017-0899-1.
S. V. Dolgov, V. A. Kazeev and B. N. Khoromskij. Direct tensor-product solution of one-dimensional elliptic equations with parameter-dependent coefficients. Mathematics and Computers in Simulation, 2018, Vol. 145, P. 136–155. DOI: 10.1016/j.matcom.2017.10.009.
V. Kazeev, I. Oseledets, M. Rakhuba and Ch. Schwab. QTT-finite-element approximation for multiscale problems I: model problems in one dimension. Advances in Computational Mathematics, 2017, Vol. 43, No. 2, P. 411–442. DOI: 10.1007/s10444-016-9491-y.
V. Kazeev and Ch. Schwab. Tensor approximation of stationary distributions of chemical reaction networks. SIAM Journal on Matrix Analysis and Applications, 2015, Vol. 36, No. 3, P. 1221–1247. DOI: 10.1137/130927218.
V. Kazeev, M. Khammash, M. Nip and Ch. Schwab. Direct solution of the chemical master equation using quantized tensor trains. PLOS Computational Biology, 2014, Vol. 10, No. 3, P. 742–758. DOI: 10.1371/journal.pcbi.1003359.
V. A. Kazeev, B. N. Khoromskij and E. E. Tyrtyshnikov. Multilevel Toeplitz matrices generated by tensor-structured vectors and convolution with logarithmic complexity. SIAM Journal on Scientific Computing, 2013, Vol. 35, No. 3, P. A1511–A1536. DOI: 10.1137/110844830.
V. Kazeev, O. Reichmann and Ch. Schwab. Low-rank tensor structure of linear diffusion operators in the TT and QTT formats. Linear Algebra and its Applications, 2013, Vol. 438, No. 11, P. 4204–4221. DOI: 10.1016/j.laa.2013.01.009.
V. A. Kazeev and B. N. Khoromskij. Low-rank explicit QTT representation of the Laplace operator and its inverse. SIAM Journal on Matrix Analysis and Applications, 2012, Vol. 33, No. 3, P. 742–758. DOI: 10.1137/100820479.
V. Kazeev and E. Tyrtyshnikov. Structure of the Hessian matrix and an economical implementation of Newton's method in the problem of canonical approximation of tensors. Computational Mathematics and Mathematical Physics, 2010, Vol. 50, No. 6, P. 927–945. DOI: 10.1134/S0965542510060011.
G. Ivanov and V. Kazeev. Minimax algorithm for constructing an optimal control strategy in differential games with a Lipschitz payoff. Computational Mathematics and Mathematical Physics, 2011, Vol. 51, No. 4, P. 550–574. DOI: 10.1134/S0965542511040075.
V. Kazeev and I. Oseledets. The tensor structure of a class of adaptive algebraic wavelet transforms. Seminar for Applied Mathematics, ETH Zurich, 2013, Report 28.
V. Kazeev, O. Reichmann and Ch. Schwab. hp-DG-QTT solution of high-dimensional degenerate diffusion equations. Seminar for Applied Mathematics, ETH Zurich, 2012, Report 11.
V. Kazeev and Ch. Schwab. Approximation of Singularities by Quantized-Tensor FEM. Proceedings in Applied Mathematics and Mechanics, 2015, Vol. 15, No. 1, P. 743–746. DOI: 10.1137/130927218.
V. Kazeev. The convergence of an algoritm solving a linear differential game with a Hausdorff-continuous cost function (in Russian). Modern Problems of Fundamental and Applied Mathematics: Collection of Scientific Works, MIPT, 2008, P. 80–98.