LEADER 04303nam 22007092 450 001 9910790142003321 005 20151005020622.0 010 $a1-107-23048-9 010 $a1-280-39412-9 010 $a9786613572042 010 $a1-139-33781-5 010 $a1-139-34026-3 010 $a1-139-34184-7 010 $a1-139-33694-0 010 $a1-139-33868-4 010 $a1-139-06130-5 035 $a(CKB)2670000000172117 035 $a(EBL)866817 035 $a(OCoLC)792684339 035 $a(SSID)ssj0000635290 035 $a(PQKBManifestationID)11437884 035 $a(PQKBTitleCode)TC0000635290 035 $a(PQKBWorkID)10652108 035 $a(PQKB)10285094 035 $a(UkCbUP)CR9781139061308 035 $a(MiAaPQ)EBC866817 035 $a(Au-PeEL)EBL866817 035 $a(CaPaEBR)ebr10558218 035 $a(CaONFJC)MIL357204 035 $a(PPN)261285297 035 $a(EXLCZ)992670000000172117 100 $a20110414d2012|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFiltering complex turbulent systems /$fAndrew J. Majda, John Harlim$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2012. 215 $a1 online resource (vii, 357 pages) $cdigital, PDF file(s) 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a1-107-01666-5 320 $aIncludes bibliographical references and index. 327 $a1. Introduction and overview: mathematical strategies for filtering turbulent systems -- 2. Filtering a stochastic complex scalar: the prototype test problem -- 3. The Kalman filter for vector systems: reduced filters and a three-dimensional toy model -- 4. Continuous and discrete Fourier series and numerical discretization -- 5. Stochastic models for turbulence -- 6. Filtering turbulent signals: plentiful observations -- 7. Filtering turbulent signals: regularly spaced sparse observations -- 8. Filtering linear stochastic PDE models with instability and model error -- 9. Strategies for filtering nonlinear systems -- 10. Filtering prototype nonlinear slow-fast systems -- 11. Filtering turbulent nonlinear dynamical systems by finite ensemble methods -- 12. Filtering turbulent nonlinear dynamical systems by linear stochastic models -- 13. Stochastic parametrized extended Kalman filter for filtering turbulent signals with model error -- 14. Filtering turbulent tracers from partial observations: an exactly solvable test model -- 15. The search for efficient skillful particle filters for high-dimensional turbulent dynamical systems. 330 $aMany natural phenomena ranging from climate through to biology are described by complex dynamical systems. Getting information about these phenomena involves filtering noisy data and prediction based on incomplete information (complicated by the sheer number of parameters involved), and often we need to do this in real time, for example for weather forecasting or pollution control. All this is further complicated by the sheer number of parameters involved leading to further problems associated with the 'curse of dimensionality' and the 'curse of small ensemble size'. The authors develop, for the first time in book form, a systematic perspective on all these issues from the standpoint of applied mathematics. The book contains enough background material from filtering, turbulence theory and numerical analysis to make the presentation self-contained and suitable for graduate courses as well as for researchers in a range of disciplines where applied mathematics is required to enlighten observations and models. 606 $aFilters (Mathematics) 606 $aDynamics$xMathematical models 606 $aTurbulence 606 $aNumerical analysis 615 0$aFilters (Mathematics) 615 0$aDynamics$xMathematical models. 615 0$aTurbulence. 615 0$aNumerical analysis. 676 $a660.2842450151 700 $aMajda$b Andrew$f1949-$0477021 702 $aHarlim$b John 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910790142003321 996 $aFiltering complex turbulent systems$93695409 997 $aUNINA