Abstract
This paper is concerned with the relationship between the sum of roots with positive real parts (SORPRP) of an even polynomial and the polynomial spectral factor of the even polynomial. The SORPRP and its relationship to Gröbner bases are firstly reviewed. Then it is shown that the system of equations satisfied by the coefficients of the polynomial spectral factor is directly related to a Gröbner basis. It is then demonstrated by means of an \( {\mathcal{H}}_2 \) optimal control problem that the above fact can be used to facilitate guaranteed accuracy computation.
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Kanno, M., Anai, H., Yokoyama, K. (2007). On the Relationship Between the Sum of Roots with Positive Real Parts and Polynomial Spectral Factorization. In: Boyanov, T., Dimova, S., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2006. Lecture Notes in Computer Science, vol 4310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70942-8_38
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DOI: https://doi.org/10.1007/978-3-540-70942-8_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70940-4
Online ISBN: 978-3-540-70942-8
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