Implicit determinant method is an effective method for some linear eigenvalue optimization problems since it solves linear systems of equations rather than eigenpairs.In this paper,we generalize the implicit determina...Implicit determinant method is an effective method for some linear eigenvalue optimization problems since it solves linear systems of equations rather than eigenpairs.In this paper,we generalize the implicit determinant method to solve an Hermitian eigenvalue optimization problem for smooth case and non-smooth case.We prove that the implicit determinant method converges locally and quadratically.Numerical experiments confirm our theoretical results and illustrate the efficiency of implicit determinant method.展开更多
Nonlinear rank-one modification of the symmetric eigenvalue problem arises from eigenvibrations of mechanical structures with elastically attached loads and calculation of the propagation modes in optical fiber. In th...Nonlinear rank-one modification of the symmetric eigenvalue problem arises from eigenvibrations of mechanical structures with elastically attached loads and calculation of the propagation modes in optical fiber. In this paper, we first study the existence and uniqueness of eigenvalues, and then investigate three numerical algorithms, namely Picard iteration, nonlinear Rayleigh quotient iteration and successive linear approximation method （SLAM）. The global convergence of the SLAM is proven under some mild assumptions. Numerical examples illustrate that the SLAM is the most robust method.展开更多
This paper aims to explore RLC equivalent circuit synthesis method forreduced-order models of interconnect circuits obtained by Krylov subspace basedmodel order reduction (MOR) methods. To guarantee pure RLC equivalen...This paper aims to explore RLC equivalent circuit synthesis method forreduced-order models of interconnect circuits obtained by Krylov subspace basedmodel order reduction (MOR) methods. To guarantee pure RLC equivalent circuitscan be synthesized, both the structures of input and output incidence matrices and theblock structure of the circuit matrices should be preserved in the reduced-order models.Block structure preserving MOR methods have been well established. In this paper,we propose an embeddable Input-Output structure Preserving Order Reduction(IOPOR) technique to further preserve the structures of input and output incidencematrices. By combining block structure preserving MOR methods and IOPOR technique,we develop an RLC equivalent circuit synthesis method RLCSYN (RLC SYNthesis).Inline diagonalization and regularization techniques are specifically proposedto enhance the robustness of inductance synthesis. The pure RLC model, high modelingaccuracy, passivity guaranteed property and SPICE simulation robustness makeRLCSYN more applicable in interconnect analysis, either for digital IC design ormixedsignal IC simulation.展开更多
基金supported by the China NSF Project (No.11971122)。
文摘Implicit determinant method is an effective method for some linear eigenvalue optimization problems since it solves linear systems of equations rather than eigenpairs.In this paper,we generalize the implicit determinant method to solve an Hermitian eigenvalue optimization problem for smooth case and non-smooth case.We prove that the implicit determinant method converges locally and quadratically.Numerical experiments confirm our theoretical results and illustrate the efficiency of implicit determinant method.
基金supported in part by NSF grants DMS-0611548 and OCI-0749217 and DOE grant DE-FC02-06ER25794supported in part by NSF of China under the contract number 10871049 and Shanghai Down project 200601.
文摘Nonlinear rank-one modification of the symmetric eigenvalue problem arises from eigenvibrations of mechanical structures with elastically attached loads and calculation of the propagation modes in optical fiber. In this paper, we first study the existence and uniqueness of eigenvalues, and then investigate three numerical algorithms, namely Picard iteration, nonlinear Rayleigh quotient iteration and successive linear approximation method （SLAM）. The global convergence of the SLAM is proven under some mild assumptions. Numerical examples illustrate that the SLAM is the most robust method.
基金NSFC research project 90307017 and 60676018partly by the National Basic Research Program of China under the grant 2005CB321701+2 种基金partly by Cross-Century Outstanding Scholar’s fund of Ministry of Education of China,partly by the doctoral program foundation of Ministry of Education of China 20050246082partly by Shanghai Dawn Project 200601partly by the National Science Foundation(NSF)under Grant CCR-0306298.
文摘This paper aims to explore RLC equivalent circuit synthesis method forreduced-order models of interconnect circuits obtained by Krylov subspace basedmodel order reduction (MOR) methods. To guarantee pure RLC equivalent circuitscan be synthesized, both the structures of input and output incidence matrices and theblock structure of the circuit matrices should be preserved in the reduced-order models.Block structure preserving MOR methods have been well established. In this paper,we propose an embeddable Input-Output structure Preserving Order Reduction(IOPOR) technique to further preserve the structures of input and output incidencematrices. By combining block structure preserving MOR methods and IOPOR technique,we develop an RLC equivalent circuit synthesis method RLCSYN (RLC SYNthesis).Inline diagonalization and regularization techniques are specifically proposedto enhance the robustness of inductance synthesis. The pure RLC model, high modelingaccuracy, passivity guaranteed property and SPICE simulation robustness makeRLCSYN more applicable in interconnect analysis, either for digital IC design ormixedsignal IC simulation.
