LEADER 04961nam 22007815 450 001 9910300256003321 005 20200703234653.0 010 $a3-319-20325-8 024 7 $a10.1007/978-3-319-20325-6 035 $a(CKB)3710000000521687 035 $a(SSID)ssj0001585011 035 $a(PQKBManifestationID)16265546 035 $a(PQKBTitleCode)TC0001585011 035 $a(PQKBWorkID)14866041 035 $a(PQKB)10431927 035 $a(DE-He213)978-3-319-20325-6 035 $a(MiAaPQ)EBC6312568 035 $a(MiAaPQ)EBC5587031 035 $a(Au-PeEL)EBL5587031 035 $a(OCoLC)921141174 035 $a(PPN)189803010 035 $a(EXLCZ)993710000000521687 100 $a20150905d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aData Assimilation $eA Mathematical Introduction /$fby Kody Law, Andrew Stuart, Konstantinos Zygalakis 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (XVIII, 242 p. 61 illus., 41 illus. in color.) 225 1 $aTexts in Applied Mathematics,$x0939-2475 ;$v62 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-20324-X 320 $aIncludes bibliographical references and index. 327 $aMathematical background -- Discrete Time: Formulation -- Discrete Time: Smoothing Algorithms -- Discrete Time: Filtering Algorithms -- Discrete Time: MATLAB Programs -- Continuous Time: Formulation -- Continuous Time: Smoothing Algorithms -- Continuous Time: Filtering Algorithms -- Continuous Time: MATLAB Programs -- Index.   . 330 $aThis book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online. The book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material is organized; the next four are concerned with discrete time dynamical systems and discrete time data; the last four are concerned with continuous time dynamical systems and continuous time data and are organized analogously to the corresponding discrete time chapters. This book is aimed at mathematical researchers interested in a systematic development of this interdisciplinary field, and at researchers from the geosciences, and a variety of other scientific fields, who use tools from data assimilation to combine data with time-dependent models. The numerous examples and illustrations make understanding of the theoretical underpinnings of data assimilation accessible. Furthermore, the examples, exercises and MATLAB software, make the book suitable for students in applied mathema tics, either through a lecture course, or through self-study.   . 410 0$aTexts in Applied Mathematics,$x0939-2475 ;$v62 606 $aDynamics 606 $aErgodic theory 606 $aProbabilities 606 $aComputer science$xMathematics 606 $aStatistics 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X 606 $aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/S17020 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aProbabilities. 615 0$aComputer science$xMathematics. 615 0$aStatistics. 615 14$aDynamical Systems and Ergodic Theory. 615 24$aProbability Theory and Stochastic Processes. 615 24$aComputational Mathematics and Numerical Analysis. 615 24$aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. 676 $a511.8 700 $aLaw$b Kody$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755620 702 $aStuart$b Andrew$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aZygalakis$b Konstantinos$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300256003321 996 $aData Assimilation$92527087 997 $aUNINA