Full Description
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, focusing on interpolation and regression models.
The methods and examples are taken from a wide range of scientific and engineering fields, including chemical engineering, electrical engineering, physics, medicine, and environmental science.
The material is based on several courses for scientists and engineers taught by the authors, and all the exercises and problems are classroom-tested. The required software is provided by way of a freely accessible program library at the University of Milan that provides up-to-date software tools for all the methods described in the book.
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
