LEADER 08515nam 22009255 450 001 9910299974603321 005 20200706210455.0 010 $a3-319-08159-4 024 7 $a10.1007/978-3-319-08159-5 035 $a(CKB)3710000000281276 035 $a(EBL)1967852 035 $a(OCoLC)898193212 035 $a(SSID)ssj0001386479 035 $a(PQKBManifestationID)11752493 035 $a(PQKBTitleCode)TC0001386479 035 $a(PQKBWorkID)11350222 035 $a(PQKB)10086409 035 $a(MiAaPQ)EBC1967852 035 $a(DE-He213)978-3-319-08159-5 035 $a(PPN)183096193 035 $a(EXLCZ)993710000000281276 100 $a20141113d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aExtraction of Quantifiable Information from Complex Systems /$fedited by Stephan Dahlke, Wolfgang Dahmen, Michael Griebel, Wolfgang Hackbusch, Klaus Ritter, Reinhold Schneider, Christoph Schwab, Harry Yserentant 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (446 p.) 225 1 $aLecture Notes in Computational Science and Engineering,$x1439-7358 ;$v102 300 $aDescription based upon print version of record. 311 $a3-319-08158-6 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aD. Belomestny, C. Bender, F. Dickmann, and N. Schweizer: Solving Stochastic Dynamic Programs by Convex Optimization and Simulation -- W. Dahmen, C. Huang, G. Kutyniok, W -- Q Lim, C. Schwab, and G. Welper: Efficient Resolution of Anisotropic Structures -- R. Ressel, P. Dülk, S. Dahlke, K. S. Kazimierski, and P. Maass: Regularity of the Parameter-to-state Map of a Parabolic Partial Differential Equation -- N. Chegini, S. Dahlke, U. Friedrich, and R. Stevenson: Piecewise Tensor Product Wavelet Bases by Extensions and Approximation Rates -- P. A. Cioica, S. Dahlke, N. Döhring, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, and R. Schilling: Adaptive Wavelet Methods for SPDEs -- M. Altmayer, S. Dereich, S. Li, T. Müller-Gronbach, A. Neuenkirch, K. Ritter and L. Yaroslavtseva: Constructive Quantization and Multilevel Algorithms for Quadrature of Stochastic Differential Equations -- O. G. Ernst, B. Sprungk, and H -- J. Starkloff: Bayesian Inverse Problems and Kalman Filters -- J. Diehl, P. Friz, H. Mai, H. Oberhauser, S. Riedel, and W. Stannat: Robustness in Stochastic Filtering and Maximum Likelihood Estimation for SDEs -- J. Garcke and I. Klompmaker: Adaptive Sparse Grids in Reinforcement Learning -- J. Ballani, L. Grasedyck, and M. Kluge: A Review on Adaptive Low-Rank Approximation Techniques in the Hierarchical Tensor Format -- M. Griebel, J. Hamaekers, and F. Heber: A Bond Order Dissection ANOVA Approach for Efficient Electronic Structure Calculations -- W. Hackbusch and R. Schneider: Tensor Spaces and Hierarchical Tensor Representations -- L. Jost, S. Setzer, and M. Hein: Nonlinear Eigenproblems in Data Analysis - Balanced Graph Cuts and the Ratio DCA-Prox -- M. Guillemard, D. Heinen, A. Iske, S. Krause-Solberg, and G. Plonka: Adaptive Approximation Algorithms for Sparse Data Representation -- T. Jahnke and V. Sunkara: Error Bound for Hybrid Models of Two-scaled Stochastic Reaction Systems -- R. Kiesel, A. Rupp, and K. Urban: Valuation of Structured Financial Products by Adaptive Multi wavelet Methods in High Dimensions -- L Kämmerer, S. Kunis, I. Melzer, D. Potts, and T. Volkmer: Computational Methods for the Fourier Analysis of Sparse High-Dimensional Functions -- E. Herrholz, D. Lorenz, G. Teschke, and D. Trede: Sparsity and Compressed Sensing in Inverse Problems -- C. Lubich: Low-Rank Dynamics -- E. Novak and D. Rudolf: Computation of Expectations by Markov Chain Monte Carlo Methods -- H. Yserentant: Regularity, Complexity, and Approximability of Electronic Wave functions -- Index. 330 $aIn April 2007, the  Deutsche Forschungsgemeinschaft (DFG) approved the  Priority Program 1324 ?Mathematical Methods for Extracting Quantifiable Information from Complex Systems.? This volume presents a comprehensive overview of the most important results obtained over the course of the program.   Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance.  Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges.   Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program.   The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics today. Since the problem of high-dimensionality appears in many fields of application, the above-mentioned synergy and cross-fertilization effects were expected to make a great impact. To be truly successful, the following issues had to be kept in mind: theoretical research and practical applications had to be developed hand in hand; moreover, it has proven necessary to combine different fields of mathematics, such as numerical analysis and computational stochastics. To keep the whole program sufficiently focused, we concentrated on specific but related fields of application that share common characteristics and, as such, they allowed us to use closely related approaches.  . 410 0$aLecture Notes in Computational Science and Engineering,$x1439-7358 ;$v102 606 $aPartial differential equations 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aComputer mathematics 606 $aNumerical analysis 606 $aProbabilities 606 $aApproximation theory 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003 606 $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aApproximations and Expansions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12023 615 0$aPartial differential equations. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aComputer mathematics. 615 0$aNumerical analysis. 615 0$aProbabilities. 615 0$aApproximation theory. 615 14$aPartial Differential Equations. 615 24$aApplications of Mathematics. 615 24$aComputational Mathematics and Numerical Analysis. 615 24$aNumerical Analysis. 615 24$aProbability Theory and Stochastic Processes. 615 24$aApproximations and Expansions. 676 $a515.35 702 $aDahlke$b Stephan$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aDahmen$b Wolfgang$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aGriebel$b Michael$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aHackbusch$b Wolfgang$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aRitter$b Klaus$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aSchneider$b Reinhold$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aSchwab$b Christoph$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aYserentant$b Harry$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299974603321 996 $aExtraction of quantifiable information from complex systems$91409860 997 $aUNINA