Desigualtats matricials lineals amb valors complexos

Sovint ens trobem davant de desigualtats matricials lineals (LMIs) on les matrius involucrades prenen valors complexos. Es ben conegut que tota LMI complexa es pot reduir a una LMI real. En aquest treball establim les propietats que permeten fer el procés de reducció de LMI complexa a LMI real de manera el més simplicada possible.Preprin

Efficient computation of frame bounds using LMI-based optimization

This correspondence presents a simple and effective method for computing the optimal frame bounds of oversampled perfect reconstruction (PR) filter banks (FBs). It first shows that computation of the optimal frame bounds for complex-valued oversampled PR FBs can be formulated as a convex optimization subject to complex-valued linear matrix inequality (LMI) constraints and solved by effective interior-point algorithms. It then deals with discrete-time Weyl-Heisenberg (WH) frames to compute bounds on the WH frames by real-valued LMI optimization. The WH frames are closely related to modulated FBs and have complex coefficients. Four examples are given to illustrate the generality and effectiveness of the proposed method

Efficient computation of frame bounds using LMI-based optimization

This correspondence presents a simple and effective method for computing the optimal frame bounds of oversampled perfect reconstruction (PR) filter banks (FBs). It first shows that computation of the optimal frame bounds for complex-valued oversampled PR FBs can be formulated as a convex optimization subject to complex-valued linear matrix inequality (LMI) constraints and solved by effective interior-point algorithms. It then deals with discrete-time Weyl-Heisenberg (WH) frames to compute bounds on the WH frames by real-valued LMI optimization. The WH frames are closely related to modulated FBs and have complex coefficients. Four examples are given to illustrate the generality and effectiveness of the proposed method