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Author Genin, Y. ♦ Hachez, Y. ♦ Nesterov, Yu. ♦ Dooren, P. Van
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Positive Polynomial ♦ Filter Design ♦ Convex Optimization Positive Polynomial ♦ Positive Polynomial Matrix ♦ Filter Design Problem ♦ Convex Optimization ♦ Real Line ♦ Former Denomination ♦ Spectral Density Function ♦ Imaginary Axis ♦ Unit Circle ♦ Many Important Optimization Problem ♦ Optimization Problem Positive Polynomial Let ♦ Nonnegative Polynomial ♦ Appropriate Transformation ♦ Control Theory ♦ Whole Real Line ♦ Trigonometric Polynomial ♦ Min Fhc ♦ Following Form ♦ Example Express Interpolation Condition ♦ Following Standard Form ♦ Linear Constraint ♦ Toeplitz Matrix ♦ Scalar Positive Polynomial ♦ Robust Control ♦ Linear Equation ♦ Interpolation Condition ♦ Certain Point ♦ Optimization Problem ♦ Stochastic Process ♦ Efficient Computational Algorithm ♦ Spectral Factorization ♦ Block Hankel ♦ Fundamental Role ♦ Relevant Class
Abstract Positive polynomial matrices play a fundamental role in systems and control theory: they represent e.g. spectral density functions of stochastic processes and show up in spectral factorizations, robust control and filter design problems. Positive polynomials obviously form a convex set and were recently studied in the area of convex optimization [1, 5]. It was shown in [2, 5] that positive polynomial matrices can be parametrized using block Hankel and Toeplitz matrices. In this paper, we use this parametrization to derive efficient computational algorithms for optimization problems over positive polynomials. Moreover, we show that filter design problems can be solved using these results.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Publisher Date 2000-01-01