The Multiple Point Global Lanczos Method for Multiple-Inputs Multiple-Outputs Interconnect Order Reductions

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

doi:10.1093/ietfec/e89-a.10.2706

The Multiple Point Global Lanczos Method for Multiple-Inputs Multiple-Outputs Interconnect Order Reductions

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

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The global Lanczos algorithm for solving the RLCG interconnect circuits is presented in this paper. This algorithm is an extension of the standard Lanczos algorithm for multiple-inputs multiple-outputs (MIMO) systems. A new matrix Krylov subspace will be developed first. By employing the congruence transformation with the matrix Krylov subspace, the two-side oblique projection-based method can be used to construct a reduced-order system. It will be shown that the system moments are still matched. The error of the 2q-th order system moment will be derived analytically. Furthermore, two novel model-order reduction techniques called the multiple point global Lanczos (MPGL) method and the adaptive-order global Lanczos (AOGL) method which are both based on the multiple point moment matching are proposed. The frequency responses using the multiple point moment matching method have higher coherence to the original system than those using the single point expansion method. Finally, simulation results on frequency domain will illustrate the feasibility and the efficiency of the proposed methods.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E89-A No.10 pp.2706-2716

Publication Date: 2006/10/01

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Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e89-a.10.2706

Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)

Category: Modelling, Systems and Simulation

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Chia-Chi CHU, Ming-Hong LAI, Wu-Shiung FENG, "The Multiple Point Global Lanczos Method for Multiple-Inputs Multiple-Outputs Interconnect Order Reductions" in IEICE TRANSACTIONS on Fundamentals, vol. E89-A, no. 10, pp. 2706-2716, October 2006, doi: 10.1093/ietfec/e89-a.10.2706.
Abstract: The global Lanczos algorithm for solving the RLCG interconnect circuits is presented in this paper. This algorithm is an extension of the standard Lanczos algorithm for multiple-inputs multiple-outputs (MIMO) systems. A new matrix Krylov subspace will be developed first. By employing the congruence transformation with the matrix Krylov subspace, the two-side oblique projection-based method can be used to construct a reduced-order system. It will be shown that the system moments are still matched. The error of the 2q-th order system moment will be derived analytically. Furthermore, two novel model-order reduction techniques called the multiple point global Lanczos (MPGL) method and the adaptive-order global Lanczos (AOGL) method which are both based on the multiple point moment matching are proposed. The frequency responses using the multiple point moment matching method have higher coherence to the original system than those using the single point expansion method. Finally, simulation results on frequency domain will illustrate the feasibility and the efficiency of the proposed methods.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.10.2706/_p

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@ARTICLE{e89-a_10_2706,
author={Chia-Chi CHU, Ming-Hong LAI, Wu-Shiung FENG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={The Multiple Point Global Lanczos Method for Multiple-Inputs Multiple-Outputs Interconnect Order Reductions},
year={2006},
volume={E89-A},
number={10},
pages={2706-2716},
abstract={The global Lanczos algorithm for solving the RLCG interconnect circuits is presented in this paper. This algorithm is an extension of the standard Lanczos algorithm for multiple-inputs multiple-outputs (MIMO) systems. A new matrix Krylov subspace will be developed first. By employing the congruence transformation with the matrix Krylov subspace, the two-side oblique projection-based method can be used to construct a reduced-order system. It will be shown that the system moments are still matched. The error of the 2q-th order system moment will be derived analytically. Furthermore, two novel model-order reduction techniques called the multiple point global Lanczos (MPGL) method and the adaptive-order global Lanczos (AOGL) method which are both based on the multiple point moment matching are proposed. The frequency responses using the multiple point moment matching method have higher coherence to the original system than those using the single point expansion method. Finally, simulation results on frequency domain will illustrate the feasibility and the efficiency of the proposed methods.},
keywords={},
doi={10.1093/ietfec/e89-a.10.2706},
ISSN={1745-1337},
month={October},}

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TY - JOUR
TI - The Multiple Point Global Lanczos Method for Multiple-Inputs Multiple-Outputs Interconnect Order Reductions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2706
EP - 2716
AU - Chia-Chi CHU
AU - Ming-Hong LAI
AU - Wu-Shiung FENG
PY - 2006
DO - 10.1093/ietfec/e89-a.10.2706
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2006
AB - The global Lanczos algorithm for solving the RLCG interconnect circuits is presented in this paper. This algorithm is an extension of the standard Lanczos algorithm for multiple-inputs multiple-outputs (MIMO) systems. A new matrix Krylov subspace will be developed first. By employing the congruence transformation with the matrix Krylov subspace, the two-side oblique projection-based method can be used to construct a reduced-order system. It will be shown that the system moments are still matched. The error of the 2q-th order system moment will be derived analytically. Furthermore, two novel model-order reduction techniques called the multiple point global Lanczos (MPGL) method and the adaptive-order global Lanczos (AOGL) method which are both based on the multiple point moment matching are proposed. The frequency responses using the multiple point moment matching method have higher coherence to the original system than those using the single point expansion method. Finally, simulation results on frequency domain will illustrate the feasibility and the efficiency of the proposed methods.
ER -