Part I: Theory and Implementation

• 2 Mathematical Considerations
  • 2.1 Nonlinear Least Squares Optimization
    • 2.1.1 Algorithm Description
    • 2.1.2 Calculation of the Jacobian Matrix
    • 2.1.3 Eigenvalues Analysis of the Approximate Hessian Matrix
    • 2.1.4 Parameters Constraints
    • 2.1.5 Parameters Accuracy and Confidence Region
    • 2.1.6 Termination Criteria
  • 2.2 Nonlinear Programming
    • 2.2.1 Sequential Linear Programming
    • 2.2.2 Sequential Quadratic Programming
  • 2.3 Empirical Model Building
    • 2.3.1 Run Matrix Generation
    • 2.3.2 Polynomial Approximation Algorithm
  • 2.4 The Monte Carlo Simulation Method
    • 2.4.1 Statistical Background
    • 2.4.2 Normal Distribution
    • 2.4.3 Multinormal Distribution
  • 2.5 Splines and TPS
    • 2.5.1 One Dimensional Spline Representation
    • 2.5.2 Tensor Product Spline Representation
• 3 Software Issues
  • 3.1 Model Objects: Syntax and Semantics
  • 3.2 Architecture
  • 3.3 Task Module