Next:
Introduction
Up:
ALIAS-C++
Previous:
How to read this
Contents
Solving with Interval Analysis
Subsections
Introduction
Interval Analysis
Mathematical background
Implementation
Problems with the interval-valuation of an expression
Dealing with infinity
Non 0-dimensional system
General purpose solving algorithm
Mathematical background
Principle
Managing the bisection and ordering
An alternative: the single bisection
Solutions and Distinct solutions
The 3B method
Simplification procedure
Implementation
Number of unknowns and functions
Type of the functions
Interval Function
The order
Storage
Accuracy
Distinct solutions
Return code
Debugging
Examples and Troubleshooting
Example 1
Example 2
Example 3
Example 4
General comments
General purpose solving algorithm with Jacobian
Mathematical background
Using the monotonicity
Improving the evaluation using the Jacobian and centered form
Single bisection mode
Implementation
Return code
Jacobian matrix
Evaluation procedure using the Jacobian
Storage
Examples
Example 1
Example 2
Example 3
Example 4
General comments
General purpose solving algorithm with Jacobian and Hessian
Mathematical background
Single bisection mode
Implementation
Hessian procedure
Storage
Improvement of the function evaluation and of the Jacobian
Return code and debug
Examples
Example 2
Example 3
Example 4
Stopping the general solving procedures
Ridder method for solving one equation
Mathematical background
Implementation
Brent method for solving one equation
Mathematical background
Implementation
Newton method for solving systems of equations
Mathematical background
Implementation
Return value
Functions
Systematic use of Newton
Krawczyk method for solving systems of equations
Mathematical background
Implementation
Solving univariate polynomial with interval analysis
Mathematical background
Implementation
Example
Solving univariate polynomial numerically
Solving trigonometric equation
Mathematical background
Implementation
Examples
Solving systems with linear and non-linear terms: the simplex method
Mathematical background
Implementation without gradient
The
NonLinear
procedure
The
CoeffLinear
procedure
Using an expansion
Example
Implementation with gradient
The
GradientNonLinear
procedure
Solving systems with determinants
Solving systems of distance equations
Principle
Implementation
Return code
Inflation and Newton scheme
Choosing the right set of equations and variables
Initial domain and simplification procedures
Filtering a system of equation
Jean-Pierre Merlet 2012-12-20
