matlab求解非线性方程组 fsolve - Solve system of nonlinear equations

作者：ariszheng 来源：转载http://tb.blog.csdn.net/TrackBack.aspx?PostId=2196865 发布时间：2008-4-12 18:20:17

减小字体增大字体

最近有人问我matlab求解方程组的问题，

下面提供了fsolve函数help,但要有几点需要注意

1.方程组的有解性

2.方程组解是否唯一

3.x0的选取，如果解不唯一，不同的x0可能会得到不同的解

fsolve - Solve system of nonlinear equations

Equation

Solves a problem specified by

F(x) = 0

for x, where x is a vector and F(x) is a function that returns a vector value.

Syntax

x = fsolve(fun,x0) x = fsolve(fun,x0,options) x = fsolve(problem) [x,fval] = fsolve(fun,x0) [x,fval,exitflag] = fsolve(...) [x,fval,exitflag,output] = fsolve(...) [x,fval,exitflag,output,jacobian] = fsolve(...)

Description

fsolve finds a root (zero) of a system of nonlinear equations.

x = fsolve(fun,x0) starts at x0 and tries to solve the equations described in fun.

x = fsolve(fun,x0,options) solves the equations with the optimization options specified in the structure options. Use optimset to set these options.

x = fsolve(problem) solves problem, where problem is a structure described in Input Arguments.

Create the structure problem by exporting a problem from Optimization Tool, as described in Exporting to the MATLAB^® Workspace.

[x,fval] = fsolve(fun,x0) returns the value of the objective function fun at the solution x.

[x,fval,exitflag] = fsolve(...) returns a value exitflag that describes the exit condition.

[x,fval,exitflag,output] = fsolve(...) returns a structure output that contains information about the optimization.

[x,fval,exitflag,output,jacobian] = fsolve(...) returns the Jacobian of fun at the solution x.

Passing Extra Parameters explains how to parameterize the objective function fun, if necessary.

Input Arguments

Function Arguments contains general descriptions of arguments passed into fsolve. This section provides function-specific details for fun and problem:

`fun`	The nonlinear system of equations to solve. `fun` is a function that accepts a vector `x` and returns a vector `F`, the nonlinear equations evaluated at `x`. The function `fun` can be specified as a function handle for an M-file function x = fsolve(@myfun,x0) where `myfun` is a MATLAB^® function such as function F = myfun(x)F = ... % Compute function values at x `fun` can also be a function handle for an anonymous function. x = fsolve(@(x)sin(x.x),x0); If the user-defined values for `x` and `F` are matrices, they are converted to a vector using linear indexing. If the Jacobian can also be computed and* the Jacobian option is `'on'`, set by options = optimset('Jacobian','on') then the function `fun` must return, in a second output argument, the Jacobian value `J`, a matrix, at `x`. If `fun` returns a vector (matrix) of `m` components and `x` has length `n`, where `n` is the length of `x0`, then the Jacobian `J` is an `m`-by-`n` matrix where `J(i,j)` is the partial derivative of `F(i)` with respect to `x(j)`. (Note that the Jacobian `J` is the transpose of the gradient of `F`.)
`problem`	`objective`	Objective function
	`x0`	Initial point for `x`
	`solver`	`'fsolve'`
	`options`	Options structure created with `optimset`

Output Arguments

Function Arguments contains general descriptions of arguments returned by fsolve. For more information on the output headings for fsolve, see Function-Specific Output Headings.

This section provides function-specific details for exitflag and output:

`exitflag`	Integer identifying the reason the algorithm terminated. The following lists the values of `exitflag` and the corresponding reasons the algorithm terminated.
	`1`	Function converged to a solution `x`.
	`2`	Change in `x` was smaller than the specified tolerance.
	`3`	Change in the residual was smaller than the specified tolerance.
	`4`	Magnitude of search direction was smaller than the specified tolerance.
	`0`	Number of iterations exceeded `options.MaxIter` or number of function evaluations exceeded `options.FunEvals`.
	`-1`	Algorithm was terminated by the output function.
	`-2`	Algorithm appears to be converging to a point that is not a root.
	`-3`	Trust radius became too small.
	`-4`	Line search cannot sufficiently decrease the residual along the current search direction.
`output`	Structure containing information about the optimization. The fields of the structure are
	`iterations`	Number of iterations taken
	`funcCount`	Number of function evaluations
	`algorithm`	Optimization algorithm used.
	`cgiterations`	Total number of PCG iterations (large-scale algorithm only)
	`stepsize`	Final displacement in `x` (Gauss-Newton and Levenberg-Marquardt algorithms)
	`firstorderopt`	Measure of first-order optimality (dogleg or large-scale algorithm, [ ] for others)
	`message`	Exit message

[1] [2] [3] [4] 下一页

[] [返回上一页] [打印]

上一篇文章：matlab 小波工具箱 wavelab

下一篇文章：matlab优化工具箱介绍

文章评论 （评论内容只代表网友观点，与本站立场无关！）