LEADER 05561nam 22007211 450 001 9910810192603321 005 20240401235240.0 010 $a3-527-66716-4 010 $a3-527-66714-8 010 $a3-527-66717-2 035 $a(CKB)2550000001163184 035 $a(EBL)1561075 035 $a(OCoLC)863673262 035 $a(SSID)ssj0001164783 035 $a(PQKBManifestationID)11768237 035 $a(PQKBTitleCode)TC0001164783 035 $a(PQKBWorkID)11197014 035 $a(PQKB)10786840 035 $a(OCoLC)868914467 035 $a(MiAaPQ)EBC1561075 035 $a(Au-PeEL)EBL1561075 035 $a(CaPaEBR)ebr10802867 035 $a(CaONFJC)MIL545322 035 $a(OCoLC)864676863 035 $a(PPN)223607258 035 $a(EXLCZ)992550000001163184 100 $a20131211h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNonlinear systems and optimization for the chemical engineer $esolving numerical problems /$fGuido Buzzi-Ferraris, Flavio Manenti 205 $a1st ed. 210 1$aWeinheim, Germany :$cWiley-VCH,$d[2014] 210 4$d©2014 215 $a1 online resource (524 p.) 300 $aDescription based upon print version of record. 311 $a3-527-33274-X 311 $a1-306-14071-4 320 $aIncludes bibliographical references and index. 327 $aNonlinear Systems and Optimization for the Chemical Engineer: Solving Numerical Problems; Contents; Preface; 1 Function Root-Finding; 1.1 Introduction; 1.2 Substitution Algorithms; 1.3 Bolzano's Algorithm; 1.4 Function Approximation; 1.4.1 Newton's Method; 1.4.2 The Secant Method; 1.4.3 Regula Falsi Method; 1.4.4 Muller's Method or Parabolic Interpolation; 1.4.5 Hyperbolic Interpolation Method; 1.4.6 Inverse Polynomial Interpolation Method; 1.4.7 Inverse Rational Interpolation Method; 1.5 Use of a Multiprocessor Machine with a Known Interval of Uncertainty 327 $a1.6 Search for an Interval of Uncertainty1.7 Stop Criteria; 1.8 Classes for Function Root-Finding; 1.9 Case Studies; 1.9.1 Calculation of the Volume of a Nonideal Gas; 1.9.2 Calculation of the Bubble Point of Vapor-Liquid Equilibrium; 1.9.3 Zero-Crossing Problem; 1.9.4 Stationary Condition in a Gravity-Flow Tank; 1.10 Tests for BzzFunctionRoot and BzzFunctionRootMP Classes; 1.11 Some Caveats; 2 One-Dimensional Optimization; 2.1 Introduction; 2.2 Measuring the Efficiency of the Search for the Minimum; 2.3 Comparison Methods; 2.4 Parabolic Interpolation; 2.5 Cubic Interpolation 327 $a2.6 Gradient-Based Methods2.7 Combination of Algorithms in a General Program; 2.8 Parallel Computations; 2.9 Search for the Interval of Uncertainty; 2.10 Stop Criteria; 2.11 Classes for One-Dimensional Minimization; 2.12 Case Studies; 2.12.1 Optimization of Unimodal Functions; 2.12.2 Optimization of a Batch Reactor; 2.12.3 Maximum Level in a Gravity-Flow Tank in Transient Conditions; 2.13 Tests; 3 Unconstrained Optimization; 3.1 Introduction; 3.1.1 Necessary and Sufficient Conditions; 3.1.2 Quadratic Functions; 3.1.3 Directions of Function Decrease 327 $a3.1.4 Comparison with the One-Dimensional Case3.1.5 Classification of Methods; 3.2 Heuristic Methods; 3.2.1 Modified Hooke-Jeeves Method; 3.2.2 The Rosenbrock Method; 3.2.3 The Nelder-Mead Simplex Method; 3.2.4 Robust Optnov Method Combined with the Simplex Method; 3.3 Gradient-Based Methods; 3.4 Conjugate Direction Methods; 3.5 Newton's Method; 3.6 Modified Newton Methods; 3.6.1 Singular or Nonpositive Definite Hessian Matrix; 3.6.2 Convergence Problems; 3.6.3 One-Dimensional Search; 3.6.4 Trust Region Methods; 3.6.5 Use of Alternative Methods; 3.7 Quasi-Newton Methods 327 $a3.8 Narrow Valley Effect3.9 Stop Criteria; 3.10 BzzMath Classes for Unconstrained Multidimensional Minimization; 3.11 Case Study; 3.11.1 Optimization of a Batch Reactor; 3.11.2 Optimal Adiabatic Bed Reactors for Sulfur Dioxide with Cold Shot Cooling; 3.11.3 Global Optimization; 3.12 Tests; 4 Large-Scale Unconstrained Optimization; 4.1 Introduction; 4.2 Collecting a Sparse Symmetric Matrix; 4.3 Ordering the Hessian Rows and Columns; 4.4 Quadratic Functions; 4.5 Hessian Evaluation; 4.6 Newton's Method; 4.7 Inexact Newton Methods; 4.8 Practical Preconditioners; 4.9 openMP Parallelization 327 $a4.10 Class for Large-Scale Unconstrained Minimization 330 $aThis third in a suite of four practical guides is an engineer's companion to using numerical methods for the solution of complex mathematical problems. It explains the theory behind current numerical methods and shows in a step-by-step fashion how to use them.The volume focuses on optimization from experimental to large-scale processes, detailing the algorithms needed to solve real-life problems. It describes the methods, innovative techniques and strategies that are all implemented in a well-established, freeware mathematical toolbox called BzzMath, which is developed and maintained by th 606 $aNonlinear systems 606 $aNumerical analysis 615 0$aNonlinear systems. 615 0$aNumerical analysis. 676 $a518 700 $aBuzzi-Ferraris$b G$g(Guido)$0888321 701 $aManenti$b Flavio$0507610 712 02$aWiley Online Library (Servicio en línea) 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910810192603321 996 $aNonlinear systems and optimization for the chemical engineer$93958318 997 $aUNINA