A convex optimization model for finding non-negative polynomials

Le, Thanh Hieu; Barel, Marc Van

doi:10.1016/j.cam.2016.01.018

Cited by 3 publications

(4 citation statements)

References 16 publications

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“…We have also developed some useful properties for low rank solutions to systems of linear matrix equations. This suggests us a reformulation of the IIR and FIR low-pass filter problems described in [17] as optimization problems over rank-one positive semidefinite matrices. In the future we will deal with this method to solve such filter design problem.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

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Low rank solutions to differentiable systems over matrices and applications

Le¹

2017

Preprint

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Differentiable systems in this paper means systems of equations that are described by differentiable real functions in real matrix variables. This paper proposes algorithms for finding minimal rank solutions to such systems over (arbitrary and/or several structured) matrices by using the Levenberg-Marquardt method (LM-method) for solving least squares problems. We then apply these algorithms to solve several engineering problems such as the low-rank matrix completion problem and the low-dimensional Euclidean embedding one. Some numerical experiments illustrate the validity of the approach.On the other hand, we provide some further properties of low rank solutions to systems linear matrix equations. This is useful when the differentiable function is linear or quadratic.

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Section: Conclusion and Discussionmentioning

confidence: 99%

“…In the future we will deal with this method to solve such filter design problem. This might be suitable because the resulting positive semidefinite matrices derived by SDP solvers in [17] are usually full rank. Obviously, this requires a much more amount of memory and complexity in comparison with rank-one setting.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Low rank solutions to differentiable systems over matrices and applications

Le¹

2017

Preprint

Self Cite

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“…From this order, the necessary coefficients can be determined through provided design equations or from tables of available coefficients, which are further used in the implementation and realization of the necessary circuits. Additionally, optimization methods have also been explored to design these types of circuits [22,23].…”

Section: Coefficient Determinationmentioning

confidence: 99%

Validation of Fractional-Order Lowpass Elliptic Responses of (1 + α)-Order Analog Filters

et al. 2018

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In this paper, fractional-order transfer functions to approximate the passband and stopband ripple characteristics of a second-order elliptic lowpass filter are designed and validated. The necessary coefficients for these transfer functions are determined through the application of a least squares fitting process. These fittings are applied to symmetrical and asymmetrical frequency ranges to evaluate how the selected approximated frequency band impacts the determined coefficients using this process and the transfer function magnitude characteristics. MATLAB simulations of ( 1 + α ) order lowpass magnitude responses are given as examples with fractional steps from α = 0.1 to α = 0.9 and compared to the second-order elliptic response. Further, MATLAB simulations of the ( 1 + α ) = 1.25 and 1.75 using all sets of coefficients are given as examples to highlight their differences. Finally, the fractional-order filter responses were validated using both SPICE simulations and experimental results using two operational amplifier topologies realized with approximated fractional-order capacitors for ( 1 + α ) = 1.2 and 1.8 order filters.

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“…Recently, as a post-LMI framework, sum of squares (SOSs) decomposition [9,10] is a promising technique which provides a new direction to tackle the mentioned drawbacks. The SOS-based approaches facilitate a systematic procedure of designing a controller with a less conservative and low complex manner through semi-definite programming.…”

Section: Introductionmentioning

confidence: 99%