# Multidimensional Root-Finding

This chapter describes functions for multidimensional root-finding (solving nonlinear systems with n equations in n unknowns). The library provides low level components for a variety of iterative solvers and convergence tests. These can be combined by the user to achieve the desired solution, with full access to the intermediate steps of the iteration. Each class of methods uses the same framework, so that you can switch between solvers at runtime without needing to recompile your program. Each instance of a solver keeps track of its own state, allowing the solvers to be used in multi-threaded programs. The solvers are based on the original Fortran library MINPACK.

The header file ``gsl_multiroots.h'` contains prototypes for the multidimensional root finding functions and related declarations.

- Overview of Multidimensional Root Finding
- Initializing the Multidimensional Solver
- Providing the multidimensional system of equations to solve
- Iteration of the multidimensional solver
- Search Stopping Parameters for the multidimensional solver
- Algorithms using Derivatives
- Algorithms without Derivatives
- Example programs for Multidimensional Root finding
- References and Further Reading for Multidimensional Root Finding