Grid Methods in Computational Real Algebraic (and Semialgebraic) Geometry

In recent years, a family of numerical algorithms to solve problems in real algebraic and semialgebraic geometry has been slowly growing. Unlike their counterparts in symbolic computation they are numerically stable. But their complexity analysis, based on the condition of the data, is radically dif...

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Bibliographic Details
Published inChinese annals of mathematics. Serie B Vol. 39; no. 2; pp. 373 - 396
Main Author Cucker, Felipe
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2018
Springer Nature B.V
Department of Mathematics, City University of Hong Kong, Hong Kong, China
Subjects
Algebra
Algorithms
Applications of Mathematics
Complexity
Computation
Ill posed problems
Mathematics
Mathematics and Statistics
Condition
65H10
Numerical algorithms
Semialgebraic geometry
14Q20
Complexity
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Summary:In recent years, a family of numerical algorithms to solve problems in real algebraic and semialgebraic geometry has been slowly growing. Unlike their counterparts in symbolic computation they are numerically stable. But their complexity analysis, based on the condition of the data, is radically different from the usual complexity analysis in symbolic computation as these numerical algorithms may run forever on a thin set of ill-posed inputs.
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-018-1070-8