Verified error bounds for isolated singular solutions of polynomial systems: case of breadth one
From MaRDI portal
Publication:385011
DOI10.1016/j.tcs.2012.10.028zbMath1291.65161arXiv1201.3443OpenAlexW2137286062MaRDI QIDQ385011
Publication date: 29 November 2013
Published in: Theoretical Computer Science (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1201.3443
Symbolic computation and algebraic computation (68W30) Numerical computation of solutions to systems of equations (65H10) Algorithms with automatic result verification (65G20) Solving polynomial systems; resultants (13P15)
Related Items
On deflation and multiplicity structure, Improved two-step Newton's method for computing simple multiple zeros of polynomial systems, Certifying solutions to overdetermined and singular polynomial systems over \(\mathbb{Q}\), A certified iterative method for isolated singular roots, VerifyRealRoots: a Matlab package for computing verified real solutions of polynomials systems of equations and inequalities, A new deflation method for verifying the isolated singular zeros of polynomial systems, On isolation of simple multiple zeros and clusters of zeros of polynomial systems, Verified error bounds for singular solutions of nonlinear systems, An improved verification algorithm for nonlinear systems of equations based on Krawczyk operator
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- 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
- Determining singular solutions of polynomial systems via symbolic-numeric reduction to geometric involutive forms
- On location and approximation of clusters of zeros: Case of embedding dimension one
- Newton's method and high order singularities
- Isolated points, duality and residues
- Quadratic Newton iteration for systems with multiplicity
- 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
- Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken
- An improved method for evaluating Max Noether conditions
- Computing Isolated Singular Solutions of Polynomial Systems: Case of Breadth One
- Multiple zeros of nonlinear systems
- On Solving Nonlinear Equations with Simple Singularities or Nearly Singular Solutions
- 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
- Convergence Acceleration for Newton’s Method at Singular Points
- A Test for Existence of Solutions to Nonlinear Systems
- On Newton’s Method for Singular Problems
- Convergence of Newton's Method for Singular Smooth and Nonsmooth Equations Using Adaptive Outer Inverses
- Numerical Polynomial Algebra
- Deflation and certified isolation of singular zeros of polynomial systems
- Computing the multiplicity structure in solving polynomial systems
- Computing the multiplicity structure from geometric involutive form
- Verified error bounds for multiple roots of systems of nonlinear equations
