#Nonlinear system of equations solver code#

/ /// /// /// public virtual bool Jacobian(double x, ref double J) / (must be overridden in inherited classes if derivative calculation supported) / /// Calculates the system's Jacobian. / /// /// /// public abstract bool Calculate(double x, ref double y) / /// Calculates equation values for given variable values. / /// Dimension (the number of equations). / public abstract class NonlinearSystem

#Nonlinear system of equations solver code#

The presented realization of the classes implemented in the MATHEMATICS library as the following:Д¬opy Code /// /// Base class for Nonlinear Equation system. In general case there must be 2 main classes: NonlinearSystem вЂ“ represents nonlinear equations system and NonlinearSolver вЂ“ represents nonlinear solver. BackgroundДЇor understanding analytical realization of nonlinear equations system solution, let us consider the general programming environment for the problem.

Calculations of analytical expressions and derivation process carried out with ANALYTICS C# library. This article introduces alternative approach, when the nonlinear system is set up in the form of analytical expressions and derivative expressions also provided in analytical form. Common realizations of computational libraries uses numerical calculation of the derivatives вЂ“ finite difference. The algorithms require calculation not only values of system equations at some point, but also the values of gradient, Jacobian or Hessian of the system, that are all some type of derivatives of the system. They realize well-known mathematical algorithms вЂ“ Newton-Raphson method, Levenberg-Marquardt method, PowellвЂ™s Dog Leg method and so on. There are many libraries for solving nonlinear equation systems.

Download nle_analytical_derivatives.rar.