Numerical Derivatives and Nonlinear Analysis

1. Methods for Numerical Differentiation.- 1.1. Wengert's Method.- 1.2. FEED (Fast and Efficient Evaluation of Derivatives).- 1.3. An Implementation of the FEED Procedure in BASIC.- 1.4. Wexler's Approach.- 1.5. Higher-Order Methods for Finding Roots.- Exercises.- 2. Nonlinear Least Squares.- 2.1. Fitting the CES Production Function.- 2.2. Passive Ranging.- 2.3. Constrained Optimization.- Appendix A. Nonlinear Least Squares Using FEED.- Appendix B. Modifications for Passive Ranging Problem.- Appendix C. Sample Output for Passive Ranging.- 3. Optimal Control.- 3.1. Control Theory.- 3.1.1. Euler-Lagrange Equations.- 3.1.2. Pontryagin's Maximum Principle.- 3.2. Numerical Methods.- 3.2.1. Newton-Raphson Method.- 3.2.2. Gradient Method.- 3.3. Description of the Subroutines.- 3.3.1. Subroutine Constant.- 3.3.2. Subroutine Add.- 3.3.3. Subroutine Multiplication.- 3.3.4. Subroutine Division.- 3.3.5. Subroutine Function.- 3.4. Examples of Optimal Control Problems.- 3.4.1. Newton-Raphson Method.- 3.4.2. Gradient Method.- 3.5. Program Listings.- 3.5.1. Simplest Problem in the Calculus of Variations.- 3.5.2. Second-Order Systems Using the Newton-Raphson Method.- 3.5.3.Nth-Order Systems Using the Gradient Method.- Exercises.- 4. System Identification.- 4.1. Quasilinearization.- 4.2. Fast and Efficient Evaluation of Derivatives (FEED).- 4.3. Computer Program.- 4.4. Numerical Results.- 4.5. Program Listing.- 5. Sukhanov's Variable Initial Value Method for Boundary Value Problems.- 5.1. Sukhanov's Initial Value Equations.- 5.1.1. Euler's Method.- 5.1.2. Runge-Kutta Integration Method.- 5.2. Automatic Derivative Evaluation.- 5.2.1. Second-Order System.- 5.2.2. Fourth-Order System.- 5.3. Examples Using Sukhanov's Method.- 5.3.1. Second-Order System.- 5.3.2. Fourth-Order System.- 5.4. Program Listing.- Exercises.- 6. Nonlinear Integral Equations.- 6.1. Derivation of the Imbedding Equations.- 6.2. Method of Computation.- 6.3. Automatic Derivative Evaluation.- 6.3.1. Subroutine Linear.- 6.3.2. Programming the Derivative Vector Operations in BASIC. ..- 6.4. Examples of Integral Equation Problems.- 6.4.1. Linear Integral Equation.- 6.4.2. Nonlinear Integral Equation.- 6.5. Program Listing.- Exercises.- References.- Author Index.