Bounding Perturbations in Zeros of Nonlinear Systems
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Summary
Algorithms for determining computationally rigorous componentwise bounds on the solutions of equations F(x, t) = 0 ∈ Rm containing parameters t ∉ Rl due to small perturbations in t when m ≤ n and when F is at most twice continuously differentiable in x and in t are described.
- Type
- article
- Published
- 2002-06-01
- Cited by
- 1
- References
- 13
- OpenAlex
- https://openalex.org/W85346632
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:36519044
Keywords
Differentiable function, Mathematics, Applied mathematics, Combinatorics, Algorithm
References
- On Bounding Solutions of Underdetermined Systems
- Numerical Toolbox for Verified Computing I
- Interval methods for systems of equations
- Numerical analysis of parametrized nonlinear equations
- Rigorous sensitivity analysis for parameter-dependent systems of equations
- The Pseudoinverse of a Rectangular or Singular Matrix and Its Application to the Solution of Systems of Linear Equations
- A generalized inverse for matrices
- Generalized inverses of linear transformations
- Interval mathematics, algebraic equations and optimization
- Generalized inverses: theory and applications
- Introduction to Interval Computation
- Interval solution of nonlinear equations using linear programming
- Rigorous Global Search: Continuous Problems
- Computing Perturbation Bounds for Nonlinear Algebraic Equations
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