Hierarchical matrix

Summary

A hierarchical matrix, or $\mathcal{H}$-matrix, is a matrix split into a hierarchy of blocks. Each block that couples well-separated groups of indices has low rank. Such matrices are stored and multiplied with a vector in about $n \log n$ operations instead of $n^2$. Approximate inverses and factorizations can be kept in the same format. This gives fast solvers for the dense matrices of integral equations and for finite element matrices.