A matrix Padé-type-Routh model reduction method for multivariable linear systems

In the present paper, the formulae for matrix Padé-type approximation were improved. The mixed model reduction method of matrix Padé-type-Routh for the multivariable linear systems was presented. A well-known example was given to illustrate that the mixed method is efficient.

Proximal Point-Like Method for Updating Simultaneously Mass and Stiffness Matrices of Finite Element Model

The problem of correcting simultaneously mass and stiffness matrices of finite element model of undamped structural systems using vibration tests is considered in this paper.The desired matrix properties,including satisfaction of the characteristic equation,symmetry,positive semidefiniteness and sparsity,are imposed as side constraints to form the optimal matrix pencil approximation problem.Using partial Lagrangian multipliers,we transform the nonlinearly constrained optimization problem into an equivalent matrix linear variational inequality,develop a proximal point-like method for solving the matrix linear variational inequality,and analyze its global convergence.Numerical results are included to illustrate the performance and application of the proposed method.

Degrees of freedom in low rank matrix estimation

The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for these types of estimators in several common settings. These results provide efficient ways of comparing different estimators and eliciting tuning parameters. Moreover, our analyses reveal new insights on the behavior of these low rank matrix estimators. These observations are of great theoretical and practical importance. In particular, they suggest that, contrary to conventional wisdom, for rank constrained estimators the total number of free parameters underestimates the degrees of freedom, whereas for nuclear norm penalization, it overestimates the degrees of freedom. In addition, when using most model selection criteria to choose the tuning parameter for nuclear norm penalization, it oftentimes suffices to entertain a finite number of candidates as opposed to a continuum of choices. Numerical examples are also presented to illustrate the practical implications of our results.

Doubling Phase Shifters for Efficient Hybrid Precoder Design in Millimeter-Wave Communication Systems

Hybrid precoding is a cost-effective approach to support directional transmissions for millimeter-wave(mmWave)communications,but its precoder design is highly complicated.In this paper,we propose a new hybrid precoder implementation,namely the double phase shifter(DPS)implementation,which enables highly tractable hybrid precoder design.Efficient algorithms are then developed for two popular hybrid precoder structures,i.e.,the fully-and partially-connected structures.For the fully-connected one,the RF-only precoding and hybrid precoding problems are formulated as a least absolute shrinkage and selection operator problem and a low-rank matrix approximation problem,respectively.In this way,computationally efficient algorithms are provided to approach the performance of the fully digital one with a small number of radio frequency(RF)chains.On the other hand,the hybrid precoder design in the partially-connected structure is identified as an eigenvalue problem.To enhance the performance of this cost-effective structure,dynamic mapping from RF chains to antennas is further proposed,for which a greedy algorithm and a modified K-means algorithm are developed.Simulation results demonstrate the performance gains of the proposed hybrid precoding algorithms over existing ones.It shows that,with the proposed DPS implementation,the fully-connected structure enjoys both satisfactory performance and low design complexity while the partially-connected one serves as an economic solution with low hardware complexity.