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This paper proposes an algebraic approach for parametric optimization which can be utilized for various problems in signal processing and control.The approach exploits the relationship between the sum of roots and polynomial spectral factorization and solves parametric polynomial spectral factorization by means of the sum of roots and the theory of… (More)

This paper is concerned with the problem of validation in the context of numerical computations in control. We explore the possibility of using computer algebra tools and interval methods to compute solutions which have guarantees on accuracy, e.g. which are not subject to unknown errors due to rounding or approximation. We demonstrate that this is possible… (More)

This paper attempts to establish a new framework of symbolic optimization of algebraic functions that is relevant to possibly a wide variety of practical application areas. The crucial aspects of the framework are (i) the suitable use of algebraic methods coupled with the discovery and exploitation of structural properties of the problem in the conversion… (More)

This paper constructs an algebraic solution approach to the algebraic Riccati equation, an important equation in signal processing and control system design. Key features of the proposed approach are the exploitation of useful structures inherent in the problem and the avoidance of Gröbner basis computation by generic algorithms. The approach extends… (More)