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Eugene E. Tyrtyshnikov

Eugene E. Tyrtyshnikov

D-Index & Metrics

Mathematics

D-Index
34
Citations
6787
World Ranking
2870
National Ranking
26

Overview

Eugene E. Tyrtyshnikov is affiliated with the Russian Academy of Sciences in the Russian Federation. Their research primarily spans the fields of Physics and Astronomy as well as Mathematics, with a significant focus on Computational Mathematics and Statistical and Nonlinear Physics. Additional subfields of study include Computational Mechanics, Atomic and Molecular Physics and Optics, and Artificial Intelligence.

The researcher's work covers several main topics, including:

  • Tensor decomposition and applications
  • Model Reduction and Neural Networks
  • Advanced Neuroimaging Techniques and Applications
  • Complex Network Analysis Techniques
  • Quantum many-body systems
  • Advanced Numerical Methods in Computational Mathematics
  • Probabilistic and Robust Engineering Design

Tyrtyshnikov has contributed publications to a range of venues, with frequent appearances in:

  • arXiv (Cornell University)
  • SIAM Journal on Scientific Computing
  • Numerical Linear Algebra with Applications
  • Nature Computational Science
  • Quantum Science and Technology

Among recent papers authored or coauthored by Tyrtyshnikov are the following:

  • A quantum-inspired approach to exploit turbulence structures, 2022, Nature Computational Science
  • Parallel time-dependent variational principle algorithm for matrix product states, 2020, Physical Review B
  • Quantum state preparation using tensor networks, 2023, Quantum Science and Technology
  • Expanding the Range of Hierarchical Equations of Motion by Tensor-Train Implementation, 2021, The Journal of Physical Chemistry B
  • Data-Driven Tensor Train Gradient Cross Approximation for Hamilton-Jacobi-Bellman Equations, 2023, SIAM Journal on Scientific Computing

Frequent coauthors associated with Tyrtyshnikov include:

  • Dmitry Savostyanov
  • Tiangang Cui
  • Dante Kalise
  • Martin Stoll
  • Michael Perelshtein

Best Publications

  • TT-cross approximation for multidimensional arrays

    Ivan Oseledets;Eugene Tyrtyshnikov

  • A Theory of Pseudoskeleton Approximations

    S.A. Goreinov;E.E. Tyrtyshnikov;N.L. Zamarashkin

  • Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions

    I. V. Oseledets;E. E. Tyrtyshnikov

  • Incomplete cross approximation in the mosaic-skeleton method

    E. E. Tyrtyshnikov

  • Mosaic-skeleton approximations

    Eugene Tyrtyshnikov

  • How to find a good submatrix

    S. Goreinov;I. Oseledets;D. Savostyanov;E. Tyrtyshnikov

  • Tucker Dimensionality Reduction of Three-Dimensional Arrays in Linear Time

    I. V. Oseledets;D. V. Savostianov;E. E. Tyrtyshnikov

  • A brief introduction to numerical analysis

    Eugene E. Tyrtyshnikov

  • Spectra of multilevel toeplitz matrices: Advanced theory via simple matrix relationships

    E.E. Tyrtyshnikov;N.L. Zamarashkin

  • Hierarchical Kronecker tensor-product approximations

    Wolfgang Hackbusch;Boris N. Khoromskij;Eugene E. Tyrtyshnikov

  • Any Circulant-Like Preconditioner for Multilevel Matrices Is Not Superlinear

    S. Serra Capizzano;E. Tyrtyshnikov

  • Approximate iterations for structured matrices

    Wolfgang Hackbusch;Boris N. Khoromskij;Eugene E. Tyrtyshnikov

  • Pseudo-skeleton approximations by matrices of maximal volume

    S. A. Goreinov;N. L. Zamarashkin;E. E. Tyrtyshnikov

  • Iterative Methods for Linear Systems: Theory and Applications

    Maxim A. Olshanskii;Eugene E. Tyrtyshnikov

  • Tensor approximations of matrices generated by asymptotically smooth functions

    E. E. Tyrtyshnikov

  • Some Remarks on the Elman Estimate for GMRES

    B. Beckermann;S. A. Goreinov;E. E. Tyrtyshnikov

  • Multilevel Toeplitz Matrices Generated by Tensor-Structured Vectors and Convolution with Logarithmic Complexity

    Vladimir A. Kazeev;Boris N. Khoromskij;Eugene E. Tyrtyshnikov

  • Circulant preconditioners with unbounded inverses

    E.E. Tyrtyshnikov

  • Kronecker-product approximations for some function-related matrices

    Eugene Tyrtyshnikov

  • Use of tensor formats in elliptic eigenvalue problems

    Wolfgang Hackbusch;Boris N. Khoromskij;Stefan A. Sauter;Eugene E. Tyrtyshnikov

Frequent Co-Authors

Ivan V. Oseledets
Ivan V. Oseledets Skolkovo Institute of Science and Technology
Boris N. Khoromskij
Boris N. Khoromskij Max Planck Institute for Mathematics in the Sciences
Maxim A. Olshanskii
Maxim A. Olshanskii University of Houston
Wolfgang Hackbusch
Wolfgang Hackbusch Max Planck Institute for Mathematics in the Sciences
Michael K. Ng
Michael K. Ng Hong Kong Baptist University
Raymond H. Chan
Raymond H. Chan Lingnan University
Dario Andrea Bini
Dario Andrea Bini University of Pisa
Paul Van Dooren
Paul Van Dooren Université Catholique de Louvain
Stefano Serra-Capizzano
Stefano Serra-Capizzano University of Insubria
Wai-Ki Ching
Wai-Ki Ching University of Hong Kong

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