Options
A block householder based algorithm for the QR decomposition of hierarchical matrices
Citation Link: https://doi.org/10.15480/882.15934
Publikationstyp
Doctoral Thesis
Date Issued
2025
Sprache
English
Author(s)
Griem, Vincent Eric
Advisor
Referee
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2025-05-09
Institute
TORE-DOI
Citation
Technische Universität Hamburg (2025)
This thesis introduces a new approach to compute QR factorizations of hierarchical matrices using block Householder transformations and a newly developed implicit storage scheme for them. The algorithm and the analysis of its numerical cost track low-rank factorizations in intermediate results. Numerical tests on several types of square matrices like 2D Laplacian boundary element matrices and different RBF kernel matrices show a good performance, although the algorithm struggles with rectangular matrices. A version of the H-LU decomposition is also implemented, demonstrating potential benefits.
Subjects
hierarchical matrices
QR decomposition
block Householder
DDC Class
519: Applied Mathematics, Probabilities
Loading...
Name
Griem_Vincent_Block_Householder_Based_QR_Decomposition_of_H-Matrices.pdf
Size
6.97 MB
Format
Adobe PDF