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008 170126t20142014sz a     b    001 0 eng d
020   $a9783319017204 (pbk.)
020   $a3319017209 (pbk.)
035   $ab14315191-39ule_inst
040   $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng
082 04$a511.42$223
084   $aAMS 49J45
084   $aAMS 74Q10
084   $aAMS 49J40
084   $aAMS 74Q05
084   $aLC QA3.L28
245 00$aModal interval analysis :$bnew tools for numerical information /$cMiguel A. Sainz ... [et al.]
264  1$aCham :$bSpringer,$cc2014
300   $axvi, 316 p. :$bill. ;$c24 cm
336   $atext$btxt$2rdacontent
337   $aunmediated$bn$2rdamedia
338   $avolume$bnc$2rdacarrier
490 1 $aLecture notes in mathematics,$x0075-8434 ;$v2091
504   $aIncludes bibliographical references (pages 307-311) and index
505 0 $a1. Intervals ; 2. Modal intervals ; 3. Modal interval extensions ; 4. Interpretability and optimality ; 5. Interval arithmetic ; 6. Equations and systems ; 7. Twins and f * algorithm ; 8. Marks ; 9. Intervals of marks ; 10. Some related problems
520 3 $aThis book presents an innovative new approach to interval analysis. Modal Interval Analysis (MIA) is an attempt to go beyond the limitations of classic intervals in terms of their structural, algebraic and logical features. The starting point of MIA is quite simple: It consists in defining a modal interval that attaches a quantifier to a classical interval and in introducing the basic relation of inclusion between modal intervals by means of the inclusion of the sets of predicates they accept. This modal approach introduces interval extensions of the real continuous functions, identifies equivalences between logical formulas and interval inclusions, and provides the semantic theorems that justify these equivalences, along with guidelines for arriving at these inclusions. Applications of these equivalences in different areas illustrate the obtained results. The book also presents a new interval object: marks, which aspire to be a new form of numerical treatment of errors in measurements and computations
650  0$aInterval analysis (Mathematics)
700 1 $aSainz, Miguel A.
907   $a.b14315191$b07-02-17$c26-01-17
912   $a991003319429707536
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996   $aModal interval analysis$91395512
997   $aUNISALENTO
998   $ale013$b26-01-17$cm$da  $e-$feng$gsz $h0$i0