LEADER 03743nam 2200541 450 001 9910466995203321 005 20200520144314.0 010 $a3-11-055367-8 024 7 $a10.1515/9783110554632 035 $a(CKB)4100000001502390 035 $a(MiAaPQ)EBC5159333 035 $a(DE-B1597)483361 035 $a(OCoLC)1024020911 035 $a(DE-B1597)9783110554632 035 $a(Au-PeEL)EBL5159333 035 $a(CaPaEBR)ebr11567026 035 $a(EXLCZ)994100000001502390 100 $a20180622d2018 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAdaptive stochastic methods $ein computational mathematics and mechanics /$fDmitry G. Arseniev, Vladimir M. Ivanov, Maxim L. Korenevsky 210 1$aBerlin ;$aBoston :$cDe Gruyter,$d2018. 215 $a1 online resource (xi, 278 pages) 311 $a3-11-055364-3 311 $a3-11-055463-1 327 $tFrontmatter -- $tPreface -- $tContents -- $tIntroduction: Statistical Computing Algorithms as a Subject of Adaptive Control -- $tPart I: Evaluation of Integrals -- $t1. Fundamentals of the Monte Carlo Method to Evaluate Definite Integrals -- $t2. Sequential Monte Carlo Method and Adaptive Integration -- $t3. Methods of Adaptive Integration Based on Piecewise Approximation -- $t4. Methods of Adaptive Integration Based on Global Approximation -- $t5. Numerical Experiments -- $t6. Adaptive Importance Sampling Method Based on Piecewise Constant Approximation -- $tPart II: Solution of Integral Equations -- $t7. Semi-Statistical Method of Solving Integral Equations Numerically -- $t8. Problem of Vibration Conductivity -- $t9. Problem on Ideal-Fluid Flow Around an Airfoil -- $t10. First Basic Problem of Elasticity Theory -- $t11. Second Basic Problem of Elasticity Theory -- $t12. Projectional and Statistical Method of Solving Integral Equations Numerically -- $tAfterword -- $tBibliography -- $tIndex 330 $aThis monograph develops adaptive stochastic methods in computational mathematics. The authors discuss the basic ideas of the algorithms and ways to analyze their properties and efficiency. Methods of evaluation of multidimensional integrals and solutions of integral equations are illustrated by multiple examples from mechanics, theory of elasticity, heat conduction and fluid dynamics. Contents Part I: Evaluation of IntegralsFundamentals of the Monte Carlo Method to Evaluate Definite IntegralsSequential Monte Carlo Method and Adaptive IntegrationMethods of Adaptive Integration Based on Piecewise ApproximationMethods of Adaptive Integration Based on Global ApproximationNumerical ExperimentsAdaptive Importance Sampling Method Based on Piecewise Constant Approximation Part II: Solution of Integral EquationsSemi-Statistical Method of Solving Integral Equations NumericallyProblem of Vibration ConductivityProblem on Ideal-Fluid Flow Around an AirfoilFirst Basic Problem of Elasticity TheorySecond Basic Problem of Elasticity TheoryProjectional and Statistical Method of Solving Integral Equations Numerically 606 $aStochastic processes 606 $aStochastic integrals 606 $aAdaptive control systems 608 $aElectronic books. 615 0$aStochastic processes. 615 0$aStochastic integrals. 615 0$aAdaptive control systems. 676 $a519.2 700 $aArsenjev$b Dmitry G.$01055099 702 $aIvanov$b Vladimir M. 702 $aKorenevskii?$b M. L$g(Maksim L?vovich), 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910466995203321 996 $aAdaptive stochastic methods$92488240 997 $aUNINA LEADER 00969nam0 22002651i 450 001 UON00349559 005 20231205104335.545 010 $a03-403-7170-6 100 $a20091209d1989 |0itac50 ba 101 $aeng 102 $aGB 105 $a|||| 1|||| 200 1 $aLetters to Alice on First Reading Jane Austen$fFay Weldon 210 $aLondon$cCoronet Books$d1989 215 $a156 p.$d18 cm. 620 $aGB$dLondon$3UONL003044 676 $a823.914$cNarrativa inglese, 1945-1999$v21 700 1$aWELDON$bFay$3UONV194744$0163404 712 $aCoronet Books$3UONV277000$4650 801 $aIT$bSOL$c20240220$gRICA 899 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$2UONSI 912 $aUON00349559 950 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$dSI Angl VI A WEL 12 $eSI LO 47425 5 12 996 $aLetters to Alice on First Reading Jane Austen$91355601 997 $aUNIOR