LRAP

This is a collection of Fortran subroutines for the constrained low-rank approximation of matrices and tensors:

• low-rank nonnegative matrix and tensor approximation (not to be confused with NMF)
• low-rank nonnegative matrix completion
• low-rank matrix and tensor approximation in the maximum norm

The algorithms are based on the method of (quasioptimal) alternating projections.

How to build

Follow the guidelines of the MARIA-Fortran project, which is used for working with low-rank matrices and tensors.

In the literature

This code was used to carry out the numerical experiments in the following articles:

• Budzinskiy S. Quasioptimal alternating projections and their use in low-rank approximation of matrices and tensors.
  arXiv: 2308.16097 (2023).
• Budzinskiy S. On the distance to low-rank matrices in the maximum norm.
  Linear Algebra Appl 688, 44–58. doi:10.1016/j.laa.2024.02.012 (2024).
• Budzinskiy S. Entrywise tensor-train approximation of large tensors via random embeddings.
  arXiv: 2403.11768 (2024).