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# Systems of Nonlinear Equations

Find roots of sets of nonlinear equations in serial or parallel

Find a solution to a multivariable nonlinear equation F(x) = 0. For problem setup, see Solver-Based Optimization Problem Setup.

## Functions

 `fsolve` Solve system of nonlinear equations `fzero` Root of nonlinear function

## Topics

### Systems of Nonlinear Equations Solutions

Nonlinear Equations with Analytic Jacobian

Example showing how to use derivatives in nonlinear equation-solving.

Nonlinear Equations with Finite-Difference Jacobian

Example showing how to solve a nonlinear system of equations without derivative information.

Nonlinear Equations with Jacobian Sparsity Pattern

Example of solving a nonlinear system of equations with known finite-difference sparsity pattern.

Nonlinear Systems with Constraints

Techniques for solving nonlinear systems of equations when there are constraints.

### Parallel Computing

What Is Parallel Computing in Optimization Toolbox?

Using multiple processors for optimization.

Using Parallel Computing in Optimization Toolbox

Improving Performance with Parallel Computing

Considerations for speeding optimizations.

### Algorithms and Options

Equation Solving Algorithms

Solving linear systems of equations, nonlinear equations in one variable, and systems of n nonlinear equations in n variables.

Optimization Options Reference

Describes optimization options.

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