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