本页对应的英文页面已更新,但尚未翻译。 若要查看最新内容,请点击此处访问英文页面。

非线性方程组

以串行或并行方式求解非线性方程组

求多变量非线性方程 F(x) = 0 的解。您也可以使用基于问题的方法求解标量方程或线性方程组,或由 F(x) = G(x) 表示的方程组(等效于使用基于求解器的方法求解 F(x) – G(x) = 0)。对于非线性方程组,求解器将方程求解问题转换为最小化 F 的分量平方和的优化问题,即 min(∑Fi2(x))。线性方程和标量方程有不同的求解算法;请参阅Equation Solving Algorithms

在开始求解优化问题之前,您必须选择合适的方法:基于问题或基于求解器。有关详细信息,请参阅 首先选择基于问题或基于求解器的方法

对于基于问题的方法,请创建问题变量,然后用这些变量表示方程。有关基于问题的求解步骤,请参阅Problem-Based Workflow for Solving Equations。要求解生成的问题,请使用 solve

有关基于求解器的求解步骤,包括定义目标函数和选择合适的求解器,请参阅基于求解器的优化问题设置

函数

全部展开

eqnproblemCreate equation problem
evaluateEvaluate optimization expression
infeasibilityConstraint violation at a point
optimeqCreate empty optimization equality array
optimvarCreate optimization variables
showDisplay information about optimization object
solveSolve optimization problem or equation problem
fsolveSolve system of nonlinear equations
fzeroRoot of nonlinear function
lsqlinSolve constrained linear least-squares problems
lsqnonlinSolve nonlinear least-squares (nonlinear data-fitting) problems

对象

EquationProblemSystem of nonlinear equations
OptimizationEqualityEqualities and equality constraints
OptimizationExpressionArithmetic or functional expression in terms of optimization variables
OptimizationVariableVariable for optimization

主题

基于问题的非线性方程组

Solve Nonlinear System of Equations, Problem-Based

Solve a system of nonlinear equations using the problem-based approach.

Solve Nonlinear System of Polynomials, Problem-Based

Solve a polynomial system of equations using the problem-based approach.

Follow Equation Solution as a Parameter Changes

Solve a sequence of problems using the previous solution as a start point.

Nonlinear System of Equations with Constraints, Problem-Based

Solve a system of nonlinear equations with constraints using the problem-based approach.

基于求解器的非线性方程组

Nonlinear Equations with Analytic Jacobian

Use derivatives in nonlinear equation solving.

Nonlinear Equations with Finite-Difference Jacobian

Solve a nonlinear system of equations without derivative information.

Nonlinear Equations with Jacobian Sparsity Pattern

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

带约束的非线性方程组

了解求解具有约束的非线性方程组的方法。

并行计算

What Is Parallel Computing in Optimization Toolbox?

Use multiple processors for optimization.

Using Parallel Computing in Optimization Toolbox

Perform gradient estimation in parallel.

Improving Performance with Parallel Computing

Investigate factors for speeding optimizations.

算法和选项

Equation Solving Algorithms

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

优化选项参考

了解优化选项。