What type of study is this?

This is a Quantitative Study study (also classified as: Experimental Study).

October 16, 2025Open Access

Hierarchical Tucker Low-Rank Matrices: Construction and Matrix-Vector Multiplication

Key Points

The HTLR matrix offers an efficient approximation for non-oscillatory kernel functions with linear complexity.
Using tensor contractions, the proposed method allows for rapid matrix-vector multiplication, achieving quasi-linear complexities.
Numerical experiments indicate that the HTLR matrix effectively balances memory usage and runtime performance.
The matrix can work on both uniform and quasi-uniform grids, enhancing its flexibility for various applications.

Abstract

In this paper, a hierarchical Tucker low-rank (HTLR) matrix is proposed to approximate non-oscillatory kernel functions in linear complexity. The HTLR matrix is based on the hierarchical matrix, with the low-rank blocks replaced by Tucker low-rank blocks. Using high-dimensional interpolation as well as tensor contractions, algorithms for the construction and matrix-vector multiplication of HTLR matrices are proposed admitting linear and quasi-linear complexities respectively. Numerical experiments demonstrate that the HTLR matrix performs well in both memory and runtime. Furthermore, the HTLR matrix can also be applied on quasi-uniform grids in addition to uniform grids, enhancing its versatility.

Hierarchical Tucker Low-Rank Matrices: Construction and Matrix-Vector Multiplication

Key Points

Abstract

Cite This Study

Also Consider

Also Consider