On isolation of simple multiple zeros and clusters of zeros of polynomial systems
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Publication:5207445
DOI10.1090/mcom/3479OpenAlexW2953875342MaRDI QIDQ5207445
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Publication date: 27 December 2019
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/mcom/3479
Symbolic computation and algebraic computation (68W30) Numerical computation of solutions to systems of equations (65H10) Multiplicity of solutions of equilibrium problems in solid mechanics (74G35) Complex singularities (32S99) Software, source code, etc. for problems pertaining to several complex variables and analytic spaces (32-04)
Related Items (6)
Inflation of poorly conditioned zeros of systems of analytic functions ⋮ Improved two-step Newton's method for computing simple multiple zeros of polynomial systems ⋮ Isolating clusters of zeros of analytic systems using arbitrary-degree inflation ⋮ Two-step Newton's method for deflation-one singular zeros of analytic systems ⋮ Squarefree normal representation of zeros of zero-dimensional polynomial systems ⋮ Locating the closest singularity in a polynomial homotopy
Cites Work
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- Verified error bounds for isolated singular solutions of polynomial systems: case of breadth one
- Computing the multiplicity structure of an isolated singular solution: case of breadth one
- Newton's method for singular nonlinear equations using approximate left and right nullspaces of the Jacobian
- Modified deflation algorithm for the solution of singular problems. I. A system of nonlinear algebraic equations
- Deflation algorithm for the multiple roots of a system of nonlinear equations
- Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients
- On location and approximation of clusters of zeros: Case of embedding dimension one
- Solving rank-deficient separable nonlinear equations
- A numerical method for branch points of a system of nonlinear algebraic equations
- Newton's method and high order singularities
- Residue currents and Bezout identities
- Isolated points, duality and residues
- Finding a cluster of zeros of univariate polynomials
- Quadratic Newton iteration for systems with multiplicity
- Numerical approximation of multiple isolated roots of analytical systems
- Certifying solutions to overdetermined and singular polynomial systems over \(\mathbb{Q}\)
- Newton's method with deflation for isolated singularities of polynomial systems
- On location and approximation of clusters of zeros of analytic functions
- Convergence of the Newton process to multiple solutions
- On deflation and multiplicity structure
- Certifying Isolated Singular Points and their Multiplicity Structure
- Computing Isolated Singular Solutions of Polynomial Systems: Case of Breadth One
- Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems
- The DMM bound
- Computational Complexity: On the Geometry of Polynomials and a Theory of Cost: II
- Multiple zeros of nonlinear systems
- Convergence Rates for Newton’s Method at Singular Points
- On Solving Nonlinear Equations with Simple Singularities or Nearly Singular Solutions
- Computational complexity. On the geometry of polynomials and a theory of cost. I
- Newton’s Method at Singular Points. I
- Newton’s Method for Singular Problems when the Dimension of the Null Space is $>1$
- Newton’s Method at Singular Points. II
- The fundamental theorem of algebra and complexity theory
- Convergence Acceleration for Newton’s Method at Singular Points
- On Newton’s Method for Singular Problems
- Existence Verification for Higher Degree Singular Zeros of Nonlinear Systems
- Existence Verification for Singular Zeros of Complex Nonlinear Systems
- On simple double zeros and badly conditioned zeros of analytic functions of 𝑛 variables
- Nuclear norm of higher-order tensors
- Existence verification for singular and nonsmooth zeros of real nonlinear systems
- Numerical Polynomial Algebra
- Complexity of Bezout’s Theorem IV: Probability of Success; Extensions
- Deflation and certified isolation of singular zeros of polynomial systems
- Computing the multiplicity structure in solving polynomial systems
- Most Tensor Problems Are NP-Hard
- Verified error bounds for multiple roots of systems of nonlinear equations
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