Book ChapterDOI
Amortized Bound for Root Isolation via Sturm Sequences
Zilin Du,Vikram Sharma,Chee Yap +2 more
- pp 113-129
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This paper presents two results on the complexity of root isolation via Sturm sequences, both of which exploit amortization arguments.Abstract:
This paper presents two results on the complexity of root isolation via Sturm sequences. Both results exploit amortization arguments.read more
Citations
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Proceedings ArticleDOI
Almost tight recursion tree bounds for the Descartes method
TL;DR: In this article, a unified framework for the Descartes method for real root isolation of square-free real polynomials is presented, and a new bound on the size of the recursion tree for polynomial with real coefficients is given.
Journal ArticleDOI
Computing real roots of real polynomials
Michael Sagraloff,Kurt Mehlhorn +1 more
TL;DR: A hybrid of the Descartes method and Newton iteration, denoted ANewDsc, is introduced, which is simpler than Pan's method, but achieves a run-time comparable to it.
Journal ArticleDOI
On the asymptotic and practical complexity of solving bivariate systems over the reals
TL;DR: This paper presents three algorithms and analyzes their asymptotic bit complexity, obtaining a bound of [email protected]?"B(N^1^4) for the purely projection-based method, and [email-protected]?", for two subresultant-based methods, which ignores polylogarithmic factors.
Proceedings ArticleDOI
A simple but exact and efficient algorithm for complex root isolation
Chee Yap,Michael Sagraloff +1 more
TL;DR: It is shown that, for the "benchmark problem" of isolating all roots of a square-free polynomial with integer coefficients, the asymptotic complexity of both algorithms EVAL and CEVAL matches that of more sophisticated real root isolation methods which are based on Descartes' Rule of Signs, Continued Fraction or Sturm sequence.
DissertationDOI
Real root isolation for exact and approximate polynomials using Descartes' rule of signs
TL;DR: The Descartes method is modified such that it can handle bitstream coefficients, which can be approximated arbitrarily well but cannot be determined exactly; the computing time and precision requirements are analyzed.
References
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Book
Introduction to Algorithms
TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
Journal ArticleDOI
Solving a Polynomial Equation: Some History and Recent Progress
TL;DR: The history of the algorithmic approach to this problem is recalled, some successful solution algorithms are reviewed, and some algorithms of 1995 are outlined that solve this problem at a surprisingly low computational cost.
Book
Fundamental Problems of Algorithmic Algebra
TL;DR: Theorems of Algebraic Numbers: Thom's Lemma and the Routh-Hurwitz Theorem are presented, which state that theorems can be applied to both classical and ideal geometry.
Journal ArticleDOI
On the worst-case arithmetic complexity of approximating zeros of polynomials
TL;DR: It is shown that with respect to a certain model of computation, the worst-case computational complexity of obtaining an e-approximation either to one, or to each, zero of arbitrary f ∈ Pd(R) is Θ(log log(R/e), that is, both upper and lower bounds are proved.