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- Set_inversion abstract "In mathematics, set inversion is the problem of characterizing the preimage X of a set Y by a function f, i.e., X = f−1(Y) = {x ∈ Rn | f(x) ∈ Y}. It can also be viewed as the problem of describing the solution set of the quantified constraint "∃ y . [f(x)=y ∧ Y(y)]", where Y(y) is a constraint, for example, an inequality, describing the set Y.In most applications, f is a function from Rn to Rp and the set Y is a box of Rp (i.e. a Cartesian product of p intervals of R). When f is nonlinear the set inversion problem can be solved using interval analysis combined with a branch-and-bound algorithm.The main idea consists in building a paving of Rp made with non-overlapping boxes. For each box [x], we perform the following tests: if f([x]) ⊂ Y we conclude that [x] ⊂ X; if f([x]) ∩ Y = ∅ we conclude that [x] ∩ X = ∅; Otherwise, the box [x] the box is bisected except if its width is smaller than a given precision.To check the two first tests, we need an interval extension (or an inclusion function) [f] for f. Classified boxes are stored into subpavings, i.e., union of non overlapping boxes. The algorithm can be made more efficient by replacing the inclusion tests by contractors.".
- Set_inversion thumbnail Wiki_ring.png?width=300.
- Set_inversion wikiPageID "39157279".
- Set_inversion wikiPageLength "4414".
- Set_inversion wikiPageOutDegree "10".
- Set_inversion wikiPageRevisionID "674048692".
- Set_inversion wikiPageWikiLink Branch_and_bound.
- Set_inversion wikiPageWikiLink Category:Topology.
- Set_inversion wikiPageWikiLink Image_(mathematics).
- Set_inversion wikiPageWikiLink Interval_analysis.
- Set_inversion wikiPageWikiLink Interval_arithmetic.
- Set_inversion wikiPageWikiLink Interval_contractor.
- Set_inversion wikiPageWikiLink Inverse_image.
- Set_inversion wikiPageWikiLink Motion_planning.
- Set_inversion wikiPageWikiLink Set_estimation.
- Set_inversion wikiPageWikiLink Subpaving.
- Set_inversion wikiPageWikiLink File:Wiki_ring.png.
- Set_inversion wikiPageWikiLinkText "SIVIA".
- Set_inversion wikiPageWikiLinkText "Set inversion".
- Set_inversion wikiPageWikiLinkText "set inversion problem".
- Set_inversion wikiPageWikiLinkText "set inversion problems".
- Set_inversion wikiPageWikiLinkText "set inversion".
- Set_inversion wikiPageWikiLinkText "set-inversion problem".
- Set_inversion hasPhotoCollection Set_inversion.
- Set_inversion wikiPageUsesTemplate Template:Reflist.
- Set_inversion subject Category:Topology.
- Set_inversion hypernym Problem.
- Set_inversion type Disease.
- Set_inversion type Field.
- Set_inversion comment "In mathematics, set inversion is the problem of characterizing the preimage X of a set Y by a function f, i.e., X = f−1(Y) = {x ∈ Rn | f(x) ∈ Y}. It can also be viewed as the problem of describing the solution set of the quantified constraint "∃ y . [f(x)=y ∧ Y(y)]", where Y(y) is a constraint, for example, an inequality, describing the set Y.In most applications, f is a function from Rn to Rp and the set Y is a box of Rp (i.e. a Cartesian product of p intervals of R).".
- Set_inversion label "Set inversion".
- Set_inversion sameAs m.0t53fcj.
- Set_inversion sameAs Q17144070.
- Set_inversion sameAs Q17144070.
- Set_inversion wasDerivedFrom Set_inversion?oldid=674048692.
- Set_inversion depiction Wiki_ring.png.
- Set_inversion isPrimaryTopicOf Set_inversion.