Numerical calculation of the multiplicity of a solution to algebraic equations

DOI10.1090/S0025-5718-98-00906-5zbMath0999.65038OpenAlexW1994403487MaRDI QIDQ4372694

Hideo Suzuki, Hidetsune Kobayashi, Yoshihiko Sakai

Publication date: 16 December 1997

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-98-00906-5

zbMATH Keywords

multiplicitysymbolic computationhomotopy methodsystem of algebraic equationsZeuthen's rule

Mathematics Subject Classification ID

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

Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety, Computing the multiplicity structure of an isolated singular solution: case of breadth one, Two-step Newton's method for deflation-one singular zeros of analytic systems, Regularization and Matrix Computation in Numerical Polynomial Algebra, Newton's method with deflation for isolated singularities of polynomial systems, A numerical-symbolic algorithm for computing the multiplicity of a component of an algebraic set, Verified error bounds for singular solutions of nonlinear systems, Multiple zeros of nonlinear systems, Determining singular solutions of polynomial systems via symbolic-numeric reduction to geometric involutive forms

Cites Work

• Finding All Solutions to a System of Polynomial Equations
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