TY - GEN
T1 - Acceleration of Vector Fitting by Reusing the Householder Reflectors in Multiple QR Factorization
AU - Chou, Chiu Chih
AU - Schutt-Aine, Jose E.
N1 - This work was supported by the National Science and Technology Council of Taiwan under Grant 110-2222-E-008-006.
PY - 2022
Y1 - 2022
N2 - 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%.
AB - 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%.
KW - Householder reflector
KW - QR factorization
KW - S parameters
KW - macromodeling
KW - rational function
KW - vector fitting
UR - http://www.scopus.com/inward/record.url?scp=85146147782&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85146147782&partnerID=8YFLogxK
U2 - 10.1109/EDAPS56906.2022.9995103
DO - 10.1109/EDAPS56906.2022.9995103
M3 - Conference contribution
AN - SCOPUS:85146147782
T3 - IEEE Electrical Design of Advanced Packaging and Systems Symposium
BT - 2022 IEEE Electrical Design of Advanced Packaging and Systems, EDAPS 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2022 IEEE Electrical Design of Advanced Packaging and Systems, EDAPS 2022
Y2 - 12 December 2022 through 14 December 2022
ER -