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A practical engineer's companion to using numerical methods for the solution of complex mathematical problems. It thus enables readers to use and implement standard numerical tools in their work, explaining the theory behind the various functions and problem solvers, while showcasing applications in diverse scientific and engineering fields. The material is based on several tried-and-tested courses for scientists and engineers taught by the authors, and all the exercises and problems are classroom-tested.The required software is freeware developed and maintained by the authors, included on the accompanying CD-ROM, together with an installation tutorial, all the examples and sample codes described in the book, as well as a host of additional examples.
List of contents
PrefaceBASIC CONCEPTSIntroductionModeling Physical PhenomenaNumber Representation on the ComputerElementary OperationsError SourcesError PropagationDecision-Making for an Optimal ProgramSelection of Programming Languages: Why C++?SOME UTILITIES IN THE BzzMATH LIBRARYIntroductionMessages and PrintingSave and LoadInteger AlgebraBzzVevtorIntArray and BzzVectorArrayBzzMatrixCoefficientsExistenceBzzMatrixExistenceBzzSymmetricMatrixCoefficientsExistenceComplex NumbersMiscellaneous UtilitiesBzzPlot.exe and BzzPlotSparse.exeLINEAR ALGEBRAIntroductionClasses for Linear AlgebraBzzVector ClassBzzMatrix ClassVector and Matrix NormsStructured MatricesSparse Unstructured MatricesSymmetric MatricesLinear Algebra OperationsSQUARE LINEAR SYSTEMSIntroductionGauss EliminationGauss TransformationClassical Gauss FactorizationAlternative MethodsConditioning of Linear SystemsBest Pivot SelectionSolution FeaturesClass for Linear System SolutionCondition Number ComputationDeterminant EvaluationInverse MatrixSparse MatricesClasses for Linear System Solution with Sparse Unstructured MatricesSTRUCTURED LINEAR SYSTEMSIntroductionSymmetric MatricesSymmetric Sparse MatricesBand MatricesDiagonal Block MatricesIterative MethodsSystems Generated by Special Physical ProblemsOVERDIMENSIONED LINEAR SYSTEMSIntroductionOrthogonal MatricesProblem ConditioningMethod of Least SquaresOrthogonal TransformationQR FactorizationClasses for QRT FactorizationSVC FactorizationClass for SVD FactorizationAdvantages of SVD FactorizationUNDERDIMENSIONED LINEAR SYSTEMSIntroductionLQ FactorizationClasses for LQ FactorizationNull SpaceMinimization with Linear ConstraintsMinimizing a Sum of Squares Subject to Linear ConstraintsSpecial Problems Solved by LQ FactorizationEIGENVALUES AND EIGENVECTORS FOR SYMMETRIC MATRICESIntroductionEigenvalues of Symmetric MatricesPower MethodInverse Power MethodInverse-Translate Power MethodJacobi MethodQR AlgorithmEigenvalues of Rank-2 MatricesITERATIVE PROCESSESIntroductionConvergence of an Iterative AlgorithmConvergence SpeedConvergence AcceleratorsExtrapolationExtrapolation MethodsClass for Numerical DerivationAPPENDIX A: Matrix ProductAPPENDIX B: EntertainmentAPPENDIX C: Basic Requirements for Using the BzzMath LibraryAPPENDIX D: Copyrights
About the author
Guido Buzzi-Ferraris is full professor of process systems engineering at Politecnico die Milano, Italy, where he holds two courses: "Methods and Numerical Applications in Chemical Engineering" and "Regression Models and Statistics". He works on numerical analysis, statistics, differential systems, and optimization. He has authored books of international relevance on numerical analysis, such as "Scientific C++" edited by Addison-Wesley, and over than 200 papers on international magazines. He is the inventor and the developer of BzzMath library, which is currently adopted by academies, R&D groups, and industries. He is permanent member of the "EFCE Working Party - Computer Aided Process Engineering" since 1969 and editorial advisory board of "Computers & Chemical Engineering" since 1987.
Flavio Manenti is assistant professor of process systems engineering at Politecnico di Milano, Italy. He obtained his academic degree and PhD at Politecnico di Milano, where he currently collaborates with Professor Buzzi-Ferraris. He holds courses on "Process Dynamics and Control of Industrial Processes" and "Supply Chain Optimization" and he works on numerical analysis, process control and optimization. He has also received international scientific awards, such as Memorial Burianec (Prague, CZ) and Excellence in Simulation (Lake Forest, CA, USA), for his research activities and scientific publications.
Summary
Die ideale Kombination: eine vollständige und wissenschaftlich exakte Beschreibung numerischer Algorithmen, die wirklich funktionieren, plus eine Gebrauchsanweisung für die praktische Umsetzung in der Technik und angewandten Mathematik.
