Solving algebraic problems with high accuracy
Proc. of the symposium on A new approach to scientific computation
Gröbner duality and multiplicities in polynomial system solving
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
SIAM Journal on Optimization
Numerical Polynomial Algebra
Computing the multiplicity structure in solving polynomial systems
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
On Location and Approximation of Clusters of Zeros of Analytic Functions
Foundations of Computational Mathematics
Newton's method with deflation for isolated singularities of polynomial systems
Theoretical Computer Science
On Location and Approximation of Clusters of Zeros: Case of Embedding Dimension One
Foundations of Computational Mathematics
Computing the multiplicity structure from geometric involutive form
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Deflation and certified isolation of singular zeros of polynomial systems
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
Computing the multiplicity structure of an isolated singular solution: Case of breadth one
Journal of Symbolic Computation
An improved method for evaluating Max Noether conditions: case of breadth one
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Computing Isolated Singular Solutions of Polynomial Systems: Case of Breadth One
SIAM Journal on Numerical Analysis
Verified error bounds for real solutions of positive-dimensional polynomial systems
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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In this paper we describe how to improve the performance of the symbolic-numeric method in [19,20] for computing the multiplicity structure and refining approximate isolated singular solutions in the breadth-one case. By introducing a parameterized deflated system with smoothing parameters, we generalize the algorithm in [33] to compute verified error bounds such that a slightly perturbed polynomial system is guaranteed to have a breadth-one multiple root within the computed bounds.