KernelyzeBase is a library, written in Fortran and with bindings to OCaml and C, that computes low-rank approximations of two-variable functions (”kernels”).
K(x,y) ~ f1(x) g1(y) + f2(x) g2(y) + . . . + fn(x) gn(y)
For many practically useful two-variable functions (”sign-regular kernels”), KernelyzeBase can compute new approximations which numerically achieve the smallest possible worst-case error among all rank-n approximations.
The worst-case error of these new approximations is much smaller than that of existing approximations such as truncated Taylor series or truncated singular function series (though KernelyzeBase also computes these more-familiar approximations, and weighting can help singular function series perform better).
The approximation computed in KernelyzeBase only applies to the single kernel case.
KernelyzePro increases the functionality of KernelyzeBase by computing approximations for the products of multiple kernels and providing a thread-safe store of approximations (suitable for use in a multithreaded application). KernelyzePro can be used as a library, but it is available as a stand-alone application or as an excel add-in. Academic licenses are available at a reduced fee.