User guide

This guide is an introduction to tensor networks and the tensor train format, not only to the library that implements them. It builds up from the problem the format solves, through the decomposition and its numerics, to the algorithms that operate in it.

Motivation explains why low-rank representations exist and introduces tensor networks. Tensor trains in numerics covers the working mechanics: construction, accuracy, complexity and quantization. Solving linear systems covers the variational solvers.

• Motivation
  • Low-rank representations
  • Tensor networks
  • References
• Tensor trains in numerics
  • Building a tensor train: TT-SVD
  • Accuracy, rounding and truncation
  • Arithmetic and complexity
  • Quantized tensor trains (QTT)
  • References
• Solving linear systems
  • ALS linear solver
  • MALS linear solver
  • AMEn linear solver
  • Choosing a solver
  • References