Acceleration of Vector Fitting by Reusing the Householder Reflectors in Multiple QR Factorization

Chiu Chih Chou, Jose E. Schutt-Aine

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The classic method of accelerating vector fitting (VF) for a multiport network is to do several small QR factorizations to extract the R22 matrices before solving the least-square system. In the literature and some open-source VF implementations, each QR factorization is performed separately. Taking a closer look at the theory, however, we can see that the first block of the matrices being factorized are the same, which means the computational cost can be reduced if the factorization of this part is skipped. To achieve this goal, however, we cannot simply call the high-level QR functions offered in many computational packages; instead, we must go down to the bottom level of QR factorization and reuse the Householder reflectors directly. In this paper, the theory and implementation of this idea is presented in detail. The theoretic flop reduction is roughly 25%, while in actual tests the time reduction may reach 60%.

Original languageEnglish (US)
Title of host publication2022 IEEE Electrical Design of Advanced Packaging and Systems, EDAPS 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781665491945
DOIs
StatePublished - 2022
Externally publishedYes
Event2022 IEEE Electrical Design of Advanced Packaging and Systems, EDAPS 2022 - Urbana, United States
Duration: Dec 12 2022Dec 14 2022

Publication series

NameIEEE Electrical Design of Advanced Packaging and Systems Symposium
Volume2022-December
ISSN (Print)2151-1225
ISSN (Electronic)2151-1233

Conference

Conference2022 IEEE Electrical Design of Advanced Packaging and Systems, EDAPS 2022
Country/TerritoryUnited States
CityUrbana
Period12/12/2212/14/22

Keywords

  • Householder reflector
  • QR factorization
  • S parameters
  • macromodeling
  • rational function
  • vector fitting

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering
  • Automotive Engineering
  • General Computer Science

Fingerprint

Dive into the research topics of 'Acceleration of Vector Fitting by Reusing the Householder Reflectors in Multiple QR Factorization'. Together they form a unique fingerprint.

Cite this