Approximate Euclidean shortest path in 3-space
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
On generalized Newton algorithms: quadratic convergence, path-following and error analysis
Selected papers of the workshop on Continuous algorithms and complexity
Weierstrass formula and zero-finding methods
Numerische Mathematik
The theory of Smale's point estimation and its applications
Proceedings of the international meeting on Linear/nonlinear iterative methods and verification of solution
Complexity and real computation
Complexity and real computation
Improvement of a convergence condition for the Durand-Kerner iteration
Journal of Computational and Applied Mathematics
Efficient exact geometric computation made easy
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Fast Multiple-Precision Evaluation of Elementary Functions
Journal of the ACM (JACM)
Pseudo approximation algorithms, with applications to optimal motion planning
Proceedings of the eighteenth annual symposium on Computational geometry
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
SIAM Journal on Matrix Analysis and Applications
Computation complexity of the euler algorithms for the roots of complex polynomials
Computation complexity of the euler algorithms for the roots of complex polynomials
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
On the boolean complexity of real root refinement
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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Smale’s notion of an approximate zero of an analytic function f: C →C is extended to take into account the errors incurred in the evaluation of the Newton operator. Call this stronger notion a robust approximate zero.. We develop a corresponding robust point estimate for such zeros: we prove that if z0∈ C satisfies α(f,z0)z0 is a robust approximate zero, with the associated zero z* lying in the closed disc ${\overline B}(z_{0},\frac{0.07}{f,z_{0}}$. Here α(f,z), γ(f,z) are standard functions in point estimates. Suppose f(z) is an L-bit integer square-free polynomial of degree d. Using our new algorithm, we can compute an n-bit absolute approximation of z*∈IR starting from a bigfloat z0, in time O[dM(n+d2(L+lg d)lg(n+L))], where M(n) is the complexity of multiplying n-bit integers.