Cover image for Fundamentals and linear algebra for the chemical engineer : solving numerical problems
Title:
Fundamentals and linear algebra for the chemical engineer : solving numerical problems
Personal Author:
Publication Information:
Weinheim : Wiley-VCH, 2010
Physical Description:
xiii, 362 p. : ill. ; 25 cm. + 1 CD-ROM (12 cm.)
ISBN:
9783527325528
General Note:
Accompanied by CD-ROM : CP 021506
Added Author:

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Call Number
Material Type
Item Category 1
Status
PSZ JB 30000010231442 QA297 B78 2010 Open Access Book Book
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Summary

Summary

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.


Author Notes

Cuido Buzzi-Ferraris is full professor of process systems engineering at Politecnico di 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, RD 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 operates in the field of Process Control, Optimization, and Supply Chain Management of Industrial Processes, where he has also received international scientific awards, such as Zdenek Burianec Memorial and Excellence in Simulation (Lake Forest, CA, USA), for his research activities and scientific publications.


Table of Contents

Prefacep. ix
1 Basic Conceptsp. 1
1.1 Introductionp. 1
1.2 Modeling Physical Phenomenap. 3
1.3 Number Representation on the Computerp. 11
1.4 Elementary Operationsp. 15
1.5 Error Sourcesp. 15
1.5.1 Model Errorp. 15
1.5.2 Approximation Errorp. 16
1.5.3 Round-Off Errorp. 16
1.5.4 Local and Propagation Errorsp. 18
1.6 Error Propagationp. 19
1.6.1 First Devicep. 21
1.6.2 Second Devicep. 23
1.6.3 Third Devicep. 24
1.7 Decision-Making for an Optimal Programp. 24
1.7.1 Check of the Physical Phenomenonp. 24
1.7.2 Mathematical Formulationp. 25
1.7.3 Selection of the Best Algorithmp. 27
1.8 Selertion of Programming Languages: Why C++?p. 36
2 Some Utilities in the BzzMath Libraryp. 39
2.1 Introductionp. 39
2.2 Messages and Printingp. 39
2.3 Save and Loadp. 40
2.4 Integer Algebrap. 42
2.4.1 BzzVectorInt Classp. 44
2.4.2 BzzMatrixIntp. 51
2.5 BzzVectorIntArray and BzzVectorArrayp. 55
2.6 BzzMatrixCoefficientsExistencep. 57
2.7 BzzMatrixExistencep. 60
2.8 BzzSymmetricMatrixCoeffidentsExistencep. 62
2.9 Complex Numbersp. 64
2.10 Miscellaneous Utilitiesp. 65
2.11 BzzPlot.exe and BzzPlotSparse.exep. 66
3 Linear Algebrap. 69
3.1 Introductionp. 69
3.2 Classes for linear Algebrap. 72
3.3 BzzVector Classp. 73
3.4 BzzMatrix Classp. 79
3.5 Vector and Matrix Normsp. 84
3.6 Structured Matricesp. 91
3.7 Sparse Unstructured Matricesp. 100
3.8 Symmetric Matricesp. 107
3.9 Linear Algebra Operationsp. 109
4 Square Linear Systemsp. 115
4.1 Introductionp. 115
4.1.1 Cramer's Methodp. 122
4.1.2 Use of Inverse Matricesp. 123
4.2 Gauss Eliminationp. 124
4.3 Gauss Transformationp. 127
4.4 Classical Gauss Factorizationp. 129
4.5 Alternative Methodsp. 133
4.6 Conditioning of linear Systemsp. 137
4.7 Best Pivot Selectionp. 149
4.8 Solution Featuresp. 154
4.9 Class for linear System Solutionp. 158
4.10 Condition Number Computationp. 165
4.11 Determinant Evaluationp. 166
4.12 Inverse Matrixp. 167
4.13 Sparse Matricesp. 170
4.14 Classes for Linear System Solution with Sparse Unstructured Matricesp. 175
5 Structured Linear Systemsp. 181
5.1 Introductionp. 181
5.2 Symmetric Matricesp. 181
5.2.1 Classes to Factorize Symmetric Matricesp. 185
5.2.2 Factorization Updatingp. 188
5.3 Symmetric Sparse Matricesp. 190
5.4 Band Matricesp. 194
5.5 Diagonal Block Matricesp. 196
5.6 Iterative Methodsp. 198
5.6.1 Richardson Methodp. 199
5.6.2 Jacobi Methodp. 199
5.6.3 Forward Gauss-Seidel Methodp. 199
5.6.4 Backward Gauss-Seidel Methodp. 200
5.6.5 Forward and Backward Gauss-Seidel Methodp. 201
5.6.6 Variantsp. 201
5.7 Systems Generated by Special Physical Problemsp. 201
5.7.1 Direct Methodsp. 202
5.7.2 Mixed Direct and Iterative (Hybrid) Methodsp. 217
6 Overdimensioned Linear Systemsp. 225
6.1 Introductionp. 225
6.2 Orthogonal Matricesp. 226
6.3 Problem Conditioningp. 227
6.4 Method of Least Squaresp. 230
6.5 Orthogonal Transformationp. 234
6.5.1 Givens Transformation Matricesp. 237
6.5.2 Householder Transformation Matricesp. 238
6.6 QR Factorizationp. 242
6.6.1 Givens Factorizationp. 241
6.6.2 Householder Factorizationp. 242
6.6.3 Square Systemsp. 243
6.6.4 Hessenberg Matrix Transformationp. 244
6.6.5 Upgrading of the QR Factorizationp. 245
6.7 Classes for QR Factorizationp. 247
6.8 SVD Factorizationp. 253
6.9 Class for SVD Factorizationp. 255
6.10 Advantages of SVD Factorizationp. 258
6.10.1 Matrices with Maximum Rank r=np. 258
6.10.2 Matrices with Rank rp. 260
6.10.3 Null Space and Range Spacep. 264
6.10.4 Data Compressionp. 267
7 Underdimensioned Linear Systemsp. 269
7.1 Introductionp. 269
7.2 LQ Factorizationp. 270
7.3 Classes for LQ Factorizationp. 272
7.4 Null Spacep. 276
7.5 Minimization with Linear Constraintsp. 281
7.6 Minimizing a Sum of Squares Subject to Linear Constraintsp. 288
7.7 Special Problems Solved by LQ Factorizationp. 290
7.7.1 Problem No.1p. 290
7.7.2 Problem No.2p. 291
7.7.3 Problem No.3p. 292
7.7.4 Problem No.4p. 293
7.7.5 Problem No.5p. 293
7.7.6 Problem No.6p. 294
7.7.7 Problem No.7p. 295
7.7.8 Problem No.8p. 296
7.7.9 Problem No.9p. 297
7.7.10 Problem No.10p. 298
7.7.11 Problem No.11p. 299
8 Eigenvalues and Eigenvectors for Symmetric Matricesp. 305
8.1 Introductionp. 305
8.2 Eigenvalues of Symmetric Matricesp. 307
8.3 Power Methodp. 309
8.4 Inverse Power Methodp. 312
8.5 Inverse-Translate Power Methodp. 314
8.6 Jacobi Methodp. 315
8.7 QR Algorithmp. 316
8.8 Eigenvalues of Rank-2 Matricesp. 319
9 Iterative Processesp. 323
9.1 Introductionp. 323
9.2 Convergence of an Iterative Algorithmp. 324
9.3 Convergence Speedp. 325
9.4 Convergence Acceleratorsp. 326
9.5 Extrapolationp. 328
9.5.1 Error Estimationp. 331
9.5.2 Solution Improvementp. 333
9.6 Extrapolation Methodsp. 334
9.6.1 Aitken Methodp. 334
9.6.2 Richardson Methodp. 335
9.6.3 Polynomial Extrapolationp. 336
9.6.4 Extrapolation with Rational Functionsp. 337
9.7 Class for Numerical Derivationp. 337
Appendix A Matrix Productp. 341
Appendix B Entertainmentp. 345
Appendix C Basic Requirements for Using the BzzMath Libraryp. 349
Appendix D Copyrightsp. 353
Referencesp. 355
Indexp. 357