Hermite's method of separation of solutions of systems of algebraic equations and its applications

DOI10.1016/0024-3795(92)90317-4zbMath0769.65023OpenAlexW2075556174MaRDI QIDQ1208262

Alexei Yu. Uteshev, Sergei G. Shulyak

Publication date: 16 May 1993

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(92)90317-4

zbMATH Keywords

quadratic formssystems of algebraic equationsHermite's methodKronecker-Poincaré indexnumber of real solutionsSturm series

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10) Real polynomials: location of zeros (26C10)

Related Items (8)

Determination of the number of roots of a polynomial lying in a given algebraic domain ⋮ Stability and distance to instability for polynomial matrix families. Complex perturbations ⋮ Universal localizing bounds for compact invariant sets of natural polynomial Hamiltonian systems ⋮ Use of polynomials in localization problems for continuous dynamical systems ⋮ Localization of periodic orbits of polynomial vector fields of even degree by linear functions ⋮ Localization of invariant compacta of autonomous systems ⋮ LOCALIZING BOUNDS FOR COMPACT INVARIANT SETS OF NONLINEAR SYSTEMS POSSESSING FIRST INTEGRALS WITH APPLICATIONS TO HAMILTONIAN SYSTEMS ⋮ On the Bézout construction of the resultant

Cites Work

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• On a theorem of Hermite and Hurwitz
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• The evaluation of the zeros of ill-conditioned polynomials. I, II
• The method of symmetric and Hermitian forms in the theory of the separation of the roots of algebraic equations
• Aperiodicity determinants expressed in terms of roots
• On the Problem of Runs
• The Critical Concomitant of Bilinear Forms

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