|  | Buzzi-Ferraris, Guido / Manenti, Flavio
Interpolation and Regression Models for the Chemical Engineer
Solving Numerical Problems
 1. Edition March 2010
89.90 Euro
2010. XIII, 429 Pages, 1 Volumes, Hardcover
45 Fig., 6 Tab.
- Practical Approach Book -
ISBN 978-3-527-32652-5 - Wiley-VCH, Weinheim
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Content
Sample Chapter
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| Short description
The perfect combination: a complete and scientifically accurate description of numerical algorithms that actually work, and a how-to guide to using them for practical problems in engineering and applied mathematics.
From the contents
Preface
INTERPOLATION
Introduction
Classes for Function Interpolation
Polynomial Interpolation
Roots-Product Form
Standard Form
Lagrange Method
Newton Method
Neville Algorithm
Hermite Polynomial Interpolation
Interpolation with Rational Functions
Inverse Interpolation
Successive Polynomial Interpolation
Two-Dimensional Curves
Orthogonal Polynomials
FUNDAMENTALS OF STATISTICS
Introduction
Fundamentals
Estimation of Expected Value
Estimation of Variance
Estimation of Standard Deviation
Outlier Detection
Relevant Probability Distributions
Correct Meaning of Statistical Tests and Confidence Regions
Nonparametric Statistics
Conditional Probability
LINEAR REGRESSIONS
Introduction
Least Sum of Squares Methods
Some Caveat
Class for Linear Regressions
Generalized Toolkit for Linear Problems
Data Modification
Data Deletion
Preliminary Analysis
Multicollinearity
Best Model Selection
Principal Components
ROBUST LINEAR REGRESSIONS
Introduction
Some Caveat
Outliers and Gross Errors
Studentized Residuals
M-Estimators
Influential Observations
Y-Outliers, X-Outliers, and F-Outliers
Secluded Observations
Robust Indices
Normality Condition
Heteroscedasticity Condition
LINEAR REGRESSION CASE STUDIES
Introduction
Ferrari F1's Test
Best Model Formulation
Outliers
Best Model Selection
Principal Components
NONLINEAR REGRESSIONS
Nonlinear Regression Problems
Some Caveat
Parameter Evaluation
BzzNonLinearRegression Class
Nonalgebraic Constraints
Algorithms for Outlier Detection
Correlations Among Model Parameters
Preventative Model Analysis
Model Discrimination
Model Collection and Model Selection
MONLINEAR REGRESSION CASE STUDIES
Introduction
One Dependent Variable with Constant Variance
Multicubic Piecewise Models
One Dependent Variable and Nonconstant Variance
More Dependent Variable and Constant Variance
More Dependent Variable and Nonconstant Variance
Model Consisting of Ordinary Differential Equations
Model Consisting of Differential Algebraic Equations
Analysis of Alternative Models
Independent Variables Subject to Experimental Error
Variables with Missing Experiments
Outliers
Independent Variables Subject to Experimental Error and Model with Outliers
REASONABLE DESIGN OF EXPERIMENTS
Introduction
Preliminary Experiments
Using Models to Suggest New Experiments
New Experiments to Improve the Parameter Estimation
Model Selection: The Bayesian Approach
New Experiments for Model Discrimination
Criterion Used in BzzNonLinearRegression Class to Generate New Experiments
APPENDIX A: Mixed-Language: Fortan and C++
APPENDIX B: Basic Requirements for Using the BzzMath Library
APPENDIX C: Copyrights
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