Complexity of linear circuits and geometry
Computational Complexity
2015-03-11 v2 Algebraic Geometry
Abstract
We use algebraic geometry to study matrix rigidity, and more generally, the complexity of computing a matrix-vector product, continuing a study initiated by Kumar, et. al. We (i) exhibit many non-obvious equations testing for (border) rigidity, (ii) compute degrees of varieties associated to rigidity, (iii) describe algebraic varieties associated to families of matrices that are expected to have super-linear rigidity, and (iv) prove results about the ideals and degrees of cones that are of interest in their own right.
Cite
@article{arxiv.1310.1362,
title = {Complexity of linear circuits and geometry},
author = {Fulvio Gesmundo and Jonathan Hauenstein and Christian Ikenmeyer and JM Landsberg},
journal= {arXiv preprint arXiv:1310.1362},
year = {2015}
}
Comments
29 pages, final version to appear in FOCM