Core Concepts
Efficiently approximate product of H2-matrices with block-relative error control.
Abstract
Non-local operators discretization leads to large matrices.
H2-matrices exploit local low-rank structures for efficiency.
Algorithm approximates product of H2-matrices with error estimates.
Specialized tree structures used for rigorous error control.
Hierarchical matrices extend applications with low complexity.
Basis trees represent matrix products efficiently.
Yield of basis trees simplifies matrix representations.
Recursive operations on basis trees for matrix multiplication.
Stats
H2-matrices reduce storage requirements to O(nk).
Fast multipole method complexity: O(nk log n).
Hierarchical matrices operations complexity: O(nkα logβ n).