Symbolic and numeric methods for exploiting structure in constructing resultant matrices

DOI10.1006/jsco.2002.0520zbMath1017.65049OpenAlexW2058393311WikidataQ57908785 ScholiaQ57908785MaRDI QIDQ1600039

Ioannis Z. Emiris, Pan, Victor Y.

Publication date: 11 June 2002

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jsco.2002.0520

zbMATH Keywords

numerical examplessymbolic computationnumerical stabilityexistence of rootsresultant matricesexact polynomial arithmetic algorithmsmultivariate nonlinear polynomial equationsNewton matricessparse elimination

Mathematics Subject Classification ID

Analysis of algorithms (68W40) Symbolic computation and algebraic computation (68W30) Numerical computation of solutions to systems of equations (65H10) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Real polynomials: location of zeros (26C10)

Related Items

Multihomogeneous resultant formulae by means of complexes, Schur aggregation for linear systems and determinants, Parametrization of approximate algebraic curves by lines, Implicitization of curves and (hyper)surfaces using predicted support, A Fast Algorithm for Computing Macaulay Null Spaces of Bivariate Polynomial Systems, Solving linear systems of equations with randomization, augmentation and aggregation, Overdetermined Weierstrass iteration and the nearest consistent system, Multilinear polynomial systems: root isolation and bit complexity, Solving over-determined systems by the subresultant method (with an appendix by Marc Chardin), Improved algorithms for computing determinants and resultants, Randomized preprocessing of homogeneous linear systems of equations, New progress in real and complex polynomial root-finding, Distance bounds of \(\varepsilon\)-points on hypersurfaces, Numerical Instability of Resultant Methods for Multidimensional Rootfinding, Matrix formulæ for resultants and discriminants of bivariate tensor-product polynomials, Rational univariate reduction via toric resultants, Lexicographic Gröbner bases of bivariate polynomials modulo a univariate one, Parametrization of approximate algebraic surfaces by lines

Uses Software

• LAPACK

Cites Work

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