Changing the topology of Tensor Networks

By Stefan Handschuh. 2012

11 citations recorded by the source corpus.

In many applications, it is needed to change the topology of a tensor network directly and without approximation. This work will introduce a general scheme that satisfies these needs. We will describe the procedure by two examples and show its efficiency in terms of memory consumption and speed in various numerical experiments. In general, we are going to provide an algorithm to add an edge to a tensor network as well as an algorithm to remove an edge unless the resulting network is a connected graph.

Citations in the corpus

• A literature survey of low‐rank tensor approximation techniques (2013, neutral): “Possibly for this reason, more general networks have not yet been considered to a large extend in the numerical analysis community for, e.g., the solution of high-dimensional PDEs, but see [75,121] for some recent mathematically oriented work.”
• Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions (2016, unknown): “The so optimized topologies yield simplified or more convenient graphical representations of a higher-order data tensor and facilitate practical applications [116, 117, 127, 288].”