Abstract
In the first section, several real root and Cauchy index counting methods are described. The second section deals with the closely related topic of Hankel matrices and quadratic forms. In the third section an important application of Cauchy index to counting complex rots with positive real part is described. The only ingredient used in later chapters of the book coming from this chapter is the computation of the Sturm-query given in Paragraph 9.1.4.
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Basu, S., Pollack, R., Roy, MF. (2003). Cauchy Index and Applications. In: Algorithms in Real Algebraic Geometry. Algorithms and Computation in Mathematics, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05355-3_10
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DOI: https://doi.org/10.1007/978-3-662-05355-3_10
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