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Parametric polynomials and eigenvalues of parametric matrices

A parametric polynomial is a polynomial whose coefficients are functions of a set of parameters (in other words it is a set of polynomials). A typical parametric polynomial is obtained when calculating the characteristic polynomial of a parametric matrix.

In this chapter we propose some algorithms to deal with the real roots of a parametric polynomial and, in some cases, with the real part of these roots. If the considered polynomial is the characteristic polynomial of a matrix we may make use of the components of the matrix.

Some of these algorithms use a primary and secondary algorithms. The secondary algorithm uses also a list of boxes which is stored in the interval matrix BoxUP.


Jean-Pierre Merlet 2012-12-20