The purpose of this research is to develop a scalable and highly optimized open source library for hierarchical low-rank approximation of dense matrices. During the previous JHPCN project we have extended the H-matrix code to perform not only matrix-vector multiplications, but also matrix-matrix multiplication, LU factorization, and QR factorization.We have also extended the parallelization to support not only OpenMP and MPI, but also batched GPU kernels and task-based parallelization. The four main goals for the fiscal year 2022 are: 1) Application of H-matrix algorithm to the tridiagonalization during the eigenvalue solvers of dense matrices, 2) Extending the GPU implementation of H-matrices to make use of TensorCores, 3) Extending the O(N) H-matrix LU factorization to distributed memory, 4) Extending the O(N) H-matrix LU factorization to LDL factorization. We were able to achieve our research goal for all 4 objectives. This year's results were published in top journals like ACM TOMS and top conferences such as SC22.