منابع مشابه
On Matrix Polynomials with Real Roots
It is proved that the roots of combinations of matrix polynomials with real roots can be recast as eigenvalues of combinations of real symmetric matrices, under certain hypotheses. The proof is based on recent solution of the Lax conjecture. Several applications and corollaries, in particular concerning hyperbolic matrix polynomials, are presented.
متن کاملOn Bounds for Real Roots of Polynomials
The computation of the real roots of univariate polynomials with real coefficients is done using several algorithmic devices. Many of them are based on the isolation of the real roots, i.e. the computation of a finite number of intervals with the property that each of them contains exactly one root. For that one of the steps is that of computing bounds for the roots. This can be realized using ...
متن کاملInequalities on real roots of polynomials
We survey the most used bounds for positive roots of polynomials and discuss their efficiency. We obtain new inequalities on roots of polynomials. Then we give new inequalities on roots of orthogonal polynomials, obtained from the differential equations satisfied by these polynomials. Mathematics subject classification (2000): 12D10, 68W30.
متن کاملSpaces of real polynomials with common roots
Let Ratk(CP) denote the space of based holomorphic maps of degree k from the Riemannian sphere S2 = C ∪∞ to the complex projective space CPn . The basepoint condition we assume is that f (∞) = [1, . . . , 1]. Such holomorphic maps are given by rational functions: Ratk(CP) = {(p0(z), . . . , pn(z)) : each pi(z) is a monic polynomial over C of degree k and such that there are no roots common to a...
متن کاملComputing real roots of real polynomials
Computing the roots of a univariate polynomial is a fundamental and long-studied problem of computational algebra with applications in mathematics, engineering, computer science, and the natural sciences. For isolating as well as for approximating all complex roots, the best algorithm known is based on an almost optimal method for approximate polynomial factorization, introduced by Pan in 2002....
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2005
ISSN: 0895-4798,1095-7162
DOI: 10.1137/040606089