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Abstract: When trying to solve quantified constraints (i.e., first-order formulas over the real numbers) exactly, one faces the following problems: First, constants coming from measurements are often only approximately given. Second, solving such constraints is in general undecidable and for special cases highly complex. Third, exact solutions are often extremely complicated symbolic expressions. In this paper we study how to do approximate computation instead - working on approximate inputs and... (Update)
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...ill posed subproblems such as the isolation of the singularities. Another problem where the algebraic number arithmetic is being a bottleneck is the one of quanti er elimination (see [7, 22] An algorithm without algebraic numbers for approximating the solution has been proposed in...
...So we will concentrate on the case where L is an (existential) quanti er. In this case we have the following function on solution sets (see [36] for the other cases) 6 De nition 4 For a variable v 2 V , the v projection operator is a function P on solution sets such that 2 P...
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BibTeX entry: (Update)
Ratschan, S. Uncertainty propagation in heterogeneous algebras for approximate quantied constraint solving. Journal of Universal Computer Science 6, 9 (2000). http://citeseer.nj.nec.com/ratschan00uncertainty.html More
@article{ ratschan00uncertainty,
author = "S. Ratschan",
title = "Uncertainty Propagation in Heterogeneous Algebras for Approximate Quantified Constraint Solving",
journal = "J.UCS: Journal of Universal Computer Science",
volume = "6",
number = "9",
pages = "861--??",
year = "2000",
url = "citeseer.nj.nec.com/ratschan00uncertainty.html" }
Citations (may not include all citations):144 A useful four-valued logic (context) - Belnap - 1977
78 Set-valued Analysis (context) - Aubin, Frankowska - 1990
58 Partial cylindrical algebraic decomposition for quanti er el.. (context) - Collins, Hong - 1991
12 Quanti er Elimination and Cylindrical Algebraic Decompositio.. (context) - Caviness, Johnson - 1998
12 Quanti er elimination for the elementary theory of real clos.. (context) - Collins - 1975
11 Computation and application of taylor polynomials with inter.. - Berz, Ho et al. - 1998
5 Computing the range of derivatives (context) - Corliss, Rall - 1991
4 Real quanti er elimination is doubly exponential (context) - Davenport, Heintz - 1988
4 Springer Verlag (context) - Algebra - 1993
2 Algorithms that still produce a solution (context) - Beltran, Castillo et al. - 1997
2 Automatically veri ed arithmetic on probability distribution.. (context) - Berleant - 1996
2 Symbolic preprocessing in interval function computing (context) - Caplat - 1979
2 Roundings and approximations in ordered sets (context) - Albrecht - 1980
1 Set functions and applications (context) - Apostolatos, Karabatzos - 1980
1 Uber einen die geometrischen Reihen betre enden Lehrsatz (context) - Cantor
1 Ane arithmetic (context) - Andrade, Comba et al. - 1994
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