Some news

A new publication has been added. To my knowledge, it is the first paper where nontrivial class of low-tensor rank matrices with inverses also of a low tensor rank is found. This class is also not very small and many useful matrices can be reduced to it.

At present, I have several pieces of work to be done: to write down all results on the optimal multiplication of binary polynomials (generated code to multiply 128-degree with polynomials with coefficients in GF(2) optimally), some more “old” results need to be written down. What I’m interested in really now, is the fast multipole method. After inspecting several papers by several people (Biros, Ying, Rokhlin and Martinsson, etc) I’ve made some conclusions. First, multipole without multipole is really possible. Second, those authors do a good job, but they do not want to read the work of others, especially the works by Tyrtyshnikov, Goreinov and Zamarashkin, the group of Hackbusch. Such reading may prevent them from reinventing the wheel in some sense. Third, the best implementation of the fast multipole lies somewhere in between those several approaches. That is what is interesting to find out —- near-to-optimal realization of the fast multipole algorithm. Maybe some tricks from the tensor approximation will be useful, especially in 3D