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Numerical Tensor Methods

Tensor Trains in Mathematics and Computer Science

Covering both theoretical foundations and applications in mathematics and engineering, this graduate textbook introduces numerical, tensor-based methods for tackling high-dimensional problems. Concepts known as tensor trains, matrix product states or hierarchical tensor networks have a range of applications in differential equations, multidimensional integration, machine learning, condensed matter physics, and theoretical chemistry.

  • The first textbook in this vibrant field of numerics.
  • Methods enabling numerical solutions to notoriously difficult high-dimensional problems.
  • Numerics examples are available as a Jupyter notebook online.

Author Information

Ivan Oseledets, Skolkovo Institute of Science and Technology and Institute of Numerical Mathematics RAS, Russia.

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Audience: Students in Mathematics, Engineering, Computer Science and Physics.