04053nam 22006975 450 99619877470331620200701170422.03-319-01721-710.1007/978-3-319-01721-1(CKB)3710000000078583(DE-He213)978-3-319-01721-1(SSID)ssj0001067700(PQKBManifestationID)11681944(PQKBTitleCode)TC0001067700(PQKBWorkID)11092888(PQKB)10824733(MiAaPQ)EBC3107068(PPN)176104704(EXLCZ)99371000000007858320131116d2014 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierModal Interval Analysis[electronic resource] New Tools for Numerical Information /by Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (XVI, 316 p. 37 illus., 3 illus. in color.) Lecture Notes in Mathematics,0075-8434 ;2091Bibliographic Level Mode of Issuance: Monograph3-319-01720-9 Includes bibliographical references and index.Intervals -- Modal Intervals -- Modal interval extensions -- Interpretability and optimality -- Interval arithmetic -- Equations and systems -- Twins and f -star algorithm -- Marks -- Intervals of marks -- Some related problems.This 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.Lecture Notes in Mathematics,0075-8434 ;2091Mathematical analysisAnalysis (Mathematics)Control engineeringNumerical analysisAnalysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12007Control and Systems Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/T19010Numeric Computinghttps://scigraph.springernature.com/ontologies/product-market-codes/I1701XMathematical analysis.Analysis (Mathematics).Control engineering.Numerical analysis.Analysis.Control and Systems Theory.Numeric Computing.515Sainz Miguel Aauthttp://id.loc.gov/vocabulary/relators/aut525064Armengol Joaquimauthttp://id.loc.gov/vocabulary/relators/autCalm Remeiauthttp://id.loc.gov/vocabulary/relators/autHerrero Pauauthttp://id.loc.gov/vocabulary/relators/autJorba Lambertauthttp://id.loc.gov/vocabulary/relators/autVehi Josepauthttp://id.loc.gov/vocabulary/relators/autBOOK996198774703316Modal interval analysis822800UNISA