Real Roots!
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چکیده
منابع مشابه
On arrangements of real roots of a real polynomial and its derivatives
We prove that all arrangements (consistent with the Rolle theorem and some other natural restrictions) of the real roots of a real polynomial and of its s-th derivative are realizable by real polynomials.
متن کاملEla Structure-preserving Schur Methods for Computing Square Roots of Real Skew-hamiltonian Matrices∗
The contribution in this paper is two-folded. First, a complete characterization is given of the square roots of a real nonsingular skew-Hamiltonian matrix W . Using the known fact that every real skew-Hamiltonian matrix has infinitely many real Hamiltonian square roots, such square roots are described. Second, a structure-exploiting method is proposed for computing square roots of W , skew-Ham...
متن کاملStructure-preserving Schur methods for computing square roots of real skew-Hamiltonian matrices
The contribution in this paper is two-folded. First, a complete characterization is given of the square roots of a real nonsingular skew-Hamiltonian matrix W . Using the known fact that every real skew-Hamiltonian matrix has infinitely many real Hamiltonian square roots, such square roots are described. Second, a structure-exploiting method is proposed for computing square roots of W , skew-Ham...
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 ...
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5 Cubic Polynomials 7 5.1 Real Roots of Multiplicity Larger Than One . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.2 One Simple Real Root . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.3 Three Simple Real Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.4 A Mixed-Type Implementation . . . . . . . . . . . . ....
متن کاملComplex roots via real roots and square roots using Routh’s stability criterion
We present a method, based on the Routh stability criterion, for finding the complex roots of polynomials with real coefficients. As in Gauss’s 1815 proof of the Fundamental Theorem of Algebra, we reduce the problem to that of finding real roots and square roots of certain associated polynomials. Unlike Gauss’s proof, our method generates these associated polynomials in an algorithmic way.
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