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    • 4. 发明申请
    • Method of developing an analogical VLSI macro model in a global Arnoldi algorithm
    • 在全局Arnoldi算法中开发类比VLSI宏模型的方法
    • US20070255538A1
    • 2007-11-01
    • US11414045
    • 2006-04-27
    • Chia-Chi ChuMing-Hong LaiWu-Shiung Feng
    • Chia-Chi ChuMing-Hong LaiWu-Shiung Feng
    • G06F17/10
    • G06F17/5036
    • A new method for MIMO RLCG interconnects model order reduction technique using the global Arnoldi algorithm is proposed that is an extension of the standard Arnoldi algorithm for MIMO systems. Under this framework, the input matrix serves as a stacked vector form and the global Arnoldi algorithm will be the standard Arnoldi algorithm applied to a new matrix pair. This new matrix Krylov subspace from the Frobenius orthonormalization process is the union of system moments. By employing the congruence transformation with this matrix Krylov subspace, the one-sided projection method can be used to construct a reduced-order system. Connections of the reduced system and the original RLCG interconnect circuits are developed. The transfer matrix residual error of reduced system is derived analytically. This error information will be a guideline for the order selection scheme. Experimental results demonstrate the feasibility and the effectiveness of the proposed method.
    • 提出了使用全局Arnoldi算法的MIMO RLCG互连模型阶数削减技术的新方法,这是MIMO系统的标准Arnoldi算法的扩展。 在这个框架下,输入矩阵用作堆栈向量形式,全局Arnoldi算法将是应用于新矩阵对的标准Arnoldi算法。 Frobenius正交化过程的新矩阵Krylov子空间是系统时刻的联合。 通过采用该矩阵Krylov子空间的一致变换,可以使用单面投影法构建一个降序系统。 开发了还原系统和原始RLCG互连电路的连接。 降低系统的传递矩阵残差是分析得出的。 此错误信息将作为订单选择方案的准则。 实验结果证明了该方法的可行性和有效性。
    • 5. 发明申请
    • Method of reducing a multiple-inputs multiple-outputs (MIMO) interconnect circuit system in a global lanczos algorithm
    • 在全局lanczos算法中减少多输入多输出(MIMO)互连电路系统的方法
    • US20080126028A1
    • 2008-05-29
    • US11527117
    • 2006-09-26
    • Chia-Chi ChuMing-Hong LaiWu-Shiung Feng
    • Chia-Chi ChuMing-Hong LaiWu-Shiung Feng
    • G06F17/10
    • G06F17/5036H04L5/20
    • A method of reducing a MIMO interconnect circuit system in a global Lanczos algorithm is used for estimation of the error margin between the original model and the reduced model of MIMO circuit system. In the algorithm, a projection matrix and then a circuit of declining order system are given. A turbulence system being added to the original system, the transfer function union is completely identical to the reduced system union given in the algorithm. It proves that the union of preceding 2q order of the transfer function of reduced system may be surely corresponding to that of original system. It is deduced from the turbulence system added to the original system that the union of preceding 2q order is equal to that of reduced system. In this invention, the algorithm is the basis of determination of the reduced circuit order in a model reduction algorithm a Krylov subspace.
    • 在全局Lanczos算法中减少MIMO互连电路系统的方法用于估计原始模型和MIMO电路系统的简化模型之间的误差容限。 在算法中,给出了一个投影矩阵,然后给出了一个下降阶系统的电路。 湍流系统被添加到原始系统中,传递函数联合与算法中给定的简化系统联合完全相同。 证明了减少系统传递函数的前2q次序的并集可以肯定地对应于原系统的传递函数。 从原始系统的湍流系统推导出,前2q级联合与减少系统的联合相等。 在本发明中,该算法是在Krylov子空间中的模型简化算法中确定简化电路顺序的基础。
    • 8. 发明授权
    • Method of determining high-speed VLSI reduced-order interconnect by non-symmetric lanczos algorithm
    • 通过非对称Lanczos算法确定高速VLSI低阶互连的方法
    • US07509243B2
    • 2009-03-24
    • US11148086
    • 2005-06-08
    • Chia-Chi ChuMing-Hong LaiWu-Shiung Feng
    • Chia-Chi ChuMing-Hong LaiWu-Shiung Feng
    • G06F17/10G06F17/50
    • G06F17/5036
    • Two-sided projection-based model reductions have become a necessity for efficient interconnect modeling and simulations in VLSI design. In order to choose the order of the reduced system that can really reflect the essential dynamics of the original interconnect, the element of reduced model of the transfer function can be considered as a stopping criteria to terminate the non-symmetric Lanczos iteration process. Furthermore, the approximate transfer function can also be expressed as the original interconnect model with some additive perturbations. The perturbation matrix only involves at most a rank-2 modification at the previous step of the non-symmetric algorithm. The information of stopping criteria will provide a guideline for the order selection scheme used in the Lanczos model-order reduction algorithm.
    • 基于双面投影的模型降低已经成为VLSI设计中高效互连建模和仿真的必要条件。 为了选择真正反映原始互连的基本动力学的简化系统的顺序,传递函数的简化模型的要素可以被认为是终止非对称Lanczos迭代过程的停止标准。 此外,近似传递函数也可以表示为具有一些附加扰动的原始互连模型。 扰动矩阵在非对称算法的前一步骤中最多仅涉及等级-2修改。 停止标准的信息将为Lanczos模型 - 订单减少算法中使用的订单选择方案提供指导。