MIMO Interconnects Order Reductions by Using the Multiple Point Adaptive-Order Rational Global Arnoldi Algorithm

Chia-Chi CHU; Ming-Hong LAI; Wu-Shiung FENG

doi:10.1093/ietele/e89-c.6.792

MIMO Interconnects Order Reductions by Using the Multiple Point Adaptive-Order Rational Global Arnoldi Algorithm

Chia-Chi CHU, Ming-Hong LAI, Wu-Shiung FENG

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We extend the adaptive-order rational Arnoldi algorithm for multiple-inputs and multiple-outputs (MIMO) interconnect model order reductions. Instead of using the standard Arnoldi algorithm for the SISO adaptive-order reduction algorithm (AORA), we study the adaptive-order rational global Arnoldi (AORGA) algorithm for MIMO model reductions. In this new algorithm, the input matrix is treated as a vector form. A new matrix Krylov subspace, generated by the global Arnoldi algorithm, will be developed by a Frobenius-orthonormal basis. By employing congruence transformation with the matrix Krylov subspace, the one-sided projection method can be used to construct a reduced-order system. It will be shown that the system moment matching can be preserved. In addition, we also show that the transfer matrix residual error of the reduced system can be derived analytically. This error information will provide a guideline for the order selection scheme. The algorithm can also be applied to the classical multiple point MIMO Pade approximation by the rational Arnoldi algorithm for multiple expansion points. Experimental results demonstrate the feasibility and the effectiveness of the proposed method.

Publication: IEICE TRANSACTIONS on Electronics Vol.E89-C No.6 pp.792-802

Publication Date: 2006/06/01

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Online ISSN: 1745-1353

DOI: 10.1093/ietele/e89-c.6.792

Type of Manuscript: Special Section PAPER (Special Section on Analog Circuit and Device Technologies)

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Chia-Chi CHU, Ming-Hong LAI, Wu-Shiung FENG, "MIMO Interconnects Order Reductions by Using the Multiple Point Adaptive-Order Rational Global Arnoldi Algorithm" in IEICE TRANSACTIONS on Electronics, vol. E89-C, no. 6, pp. 792-802, June 2006, doi: 10.1093/ietele/e89-c.6.792.
Abstract: We extend the adaptive-order rational Arnoldi algorithm for multiple-inputs and multiple-outputs (MIMO) interconnect model order reductions. Instead of using the standard Arnoldi algorithm for the SISO adaptive-order reduction algorithm (AORA), we study the adaptive-order rational global Arnoldi (AORGA) algorithm for MIMO model reductions. In this new algorithm, the input matrix is treated as a vector form. A new matrix Krylov subspace, generated by the global Arnoldi algorithm, will be developed by a Frobenius-orthonormal basis. By employing congruence transformation with the matrix Krylov subspace, the one-sided projection method can be used to construct a reduced-order system. It will be shown that the system moment matching can be preserved. In addition, we also show that the transfer matrix residual error of the reduced system can be derived analytically. This error information will provide a guideline for the order selection scheme. The algorithm can also be applied to the classical multiple point MIMO Pade approximation by the rational Arnoldi algorithm for multiple expansion points. Experimental results demonstrate the feasibility and the effectiveness of the proposed method.
URL: https://globals.ieice.org/en_transactions/electronics/10.1093/ietele/e89-c.6.792/_p

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@ARTICLE{e89-c_6_792,
author={Chia-Chi CHU, Ming-Hong LAI, Wu-Shiung FENG, },
journal={IEICE TRANSACTIONS on Electronics},
title={MIMO Interconnects Order Reductions by Using the Multiple Point Adaptive-Order Rational Global Arnoldi Algorithm},
year={2006},
volume={E89-C},
number={6},
pages={792-802},
abstract={We extend the adaptive-order rational Arnoldi algorithm for multiple-inputs and multiple-outputs (MIMO) interconnect model order reductions. Instead of using the standard Arnoldi algorithm for the SISO adaptive-order reduction algorithm (AORA), we study the adaptive-order rational global Arnoldi (AORGA) algorithm for MIMO model reductions. In this new algorithm, the input matrix is treated as a vector form. A new matrix Krylov subspace, generated by the global Arnoldi algorithm, will be developed by a Frobenius-orthonormal basis. By employing congruence transformation with the matrix Krylov subspace, the one-sided projection method can be used to construct a reduced-order system. It will be shown that the system moment matching can be preserved. In addition, we also show that the transfer matrix residual error of the reduced system can be derived analytically. This error information will provide a guideline for the order selection scheme. The algorithm can also be applied to the classical multiple point MIMO Pade approximation by the rational Arnoldi algorithm for multiple expansion points. Experimental results demonstrate the feasibility and the effectiveness of the proposed method.},
keywords={},
doi={10.1093/ietele/e89-c.6.792},
ISSN={1745-1353},
month={June},}

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TY - JOUR
TI - MIMO Interconnects Order Reductions by Using the Multiple Point Adaptive-Order Rational Global Arnoldi Algorithm
T2 - IEICE TRANSACTIONS on Electronics
SP - 792
EP - 802
AU - Chia-Chi CHU
AU - Ming-Hong LAI
AU - Wu-Shiung FENG
PY - 2006
DO - 10.1093/ietele/e89-c.6.792
JO - IEICE TRANSACTIONS on Electronics
SN - 1745-1353
VL - E89-C
IS - 6
JA - IEICE TRANSACTIONS on Electronics
Y1 - June 2006
AB - We extend the adaptive-order rational Arnoldi algorithm for multiple-inputs and multiple-outputs (MIMO) interconnect model order reductions. Instead of using the standard Arnoldi algorithm for the SISO adaptive-order reduction algorithm (AORA), we study the adaptive-order rational global Arnoldi (AORGA) algorithm for MIMO model reductions. In this new algorithm, the input matrix is treated as a vector form. A new matrix Krylov subspace, generated by the global Arnoldi algorithm, will be developed by a Frobenius-orthonormal basis. By employing congruence transformation with the matrix Krylov subspace, the one-sided projection method can be used to construct a reduced-order system. It will be shown that the system moment matching can be preserved. In addition, we also show that the transfer matrix residual error of the reduced system can be derived analytically. This error information will provide a guideline for the order selection scheme. The algorithm can also be applied to the classical multiple point MIMO Pade approximation by the rational Arnoldi algorithm for multiple expansion points. Experimental results demonstrate the feasibility and the effectiveness of the proposed method.
ER -