Programs that urgently require MATLAB to solve systems of nonlinear equations

Oops, not really.

If I were you, I'd see if it was convergent first.

After you change it, the general formula is still wrong.

Let me tell you what I think.

You construct a n*3 0 matrix, with rows 1, 2, and 3 representing the values of x, y, and z, respectively, and then loop around to eliminate the need to iterate and replace the values of the corresponding positions in the original matrix.

Then each cycle can be considered as solving a nonlinear equation once, so that the final result comes out.

Because the formula you gave is incorrect, I can't program it, so I'll just talk about the idea.

Use the solve function.

For example: x 2 + y 3 = 10

x^3-y^2=1

where x and y are the unknown quantities of the system of equations.

In the MATLAB Naming window, type:

syms x y

x y]=solve('x^2+y=10','x^2-y^2=1','x','y')

The output evaluates to: x =

y = <> precautions. solve is a basic built-in function for symbolically solving equations, and the return type is a matrix of symbolic variables (m nm n sym). When the sign cannot be solved, a warning is thrown and a numerical solution is output.

The basic form is: solve(eqn, var, name, val);

eqn is the symbolic expression, symbolic variable, and the function handle of the symbolic expression, var is the unknown quantity; name is an additional requirement, val is its value, and a one-dimensional equation can be solved with solve. For polynomials, solve can return all of its values.

func1 = x)x^3 - 20*x^2 - 25*x + 500;% creates a function handle. The variables in the handle are not symbolic variables and do not need to be defined.

syms x exp1;% defines symbolic variable x, exp1;

exp1 = x^3 - 20*x^2 - 25*x + 500;% symbolic expressions, which contain symbolic variables. Symbolic variables must first be defined on the previous line.

solve(exp1 ==0, x) % command line input a, passing in an equation containing a symbolic expression, x is the required variable.

solve(exp1, x) % is entered into b on the command line, and a symbolic expression is passed in, and the function defaults to its zero point.

solve(func1(x), x) % command line input c, passing in the parameter func1(x) is equivalent to the symbolic expression passed in, exactly the same as entering b.

solve(func1(x) =0, x) % command line input d, which is exactly the same as a.

solve(func1, x) % command line input e, pass in the parameter func1, which is a function handle, and the function defaults to zero.

ans = command-line output, three solutions, and a 3*1 symbol vector. The above five inputs and outputs are exactly the same.

For an unsignable solution to the zero-point equation of a function, solve throws a warning and returns a numerical solution:

exp1 = atan(x) -x - 1;% is an expression for finding the zero point unsigned.

solve(exp1 ==0, x) %command-line input.

Command line output:

Warning: cannot solve symbolically returning a numeric approximation =

You can use the solve function. Refer to the following below:

For example: x 2 + y 3 = 10

x^3-y^2=1

where x and y are the unknown quantities of the system of equations, enter y = in the naming window of MATLAB

syms x y

x y]=solve('x^2+y=10','x^2-y^2=1','x','y'The output evaluates to: x =

Summary. Hello, happy to answer your <>

A system of linear equations can be expressed in the form of ax=b, where a is a matrix of coefficients, x is an unknown vector, and b is a known vector. For a system of n-element linear equations, the value of x can be solved by ax=b if the coefficient matrix a satisfies the reversibility condition. In MATLAB, systems of linear equations can be solved using the " " sign or the inv() function.

The solution of nonlinear equations is usually not directly solved, and the solution needs to be approximated by iterative methods. In MATLAB, commonly used functions to solve nonlinear equations are fsolve(), fminsearch(), etc. Among them, the fsolve() function can solve a system of multivariate nonlinear equations, which is iteratively iterated using Newton's method, and needs to provide the initial value and the function handle of the system of equations.

The fminsearch() function can solve a system of nonlinear equations by minimizing the objective function, and the initial value and the function handle of the objective function need to be provided.

MATLAB solves systems of linear and nonlinear equations.

Experiment report. How to write.

Hello, happy to answer your <>

A system of linear equations can be expressed as the form ax=b, where a is the coefficient matrix, x is the unknown vector, and b is the known vector shouting gesture key. For a system of n-element linear equations, if the coefficient matrix a satisfies the reversibility condition, the value of x can be solved by ax=b. In MATLAB, systems of linear equations can be solved using the " " sign or the inv() function.

The solution of nonlinear equations is usually not directly solved, and the solution needs to be approximated by iterative methods. In MATLAB, commonly used functions to solve nonlinear equations are fsolve(), fminsearch(), etc. Among them, the fsolve() function can solve a system of multivariate nonlinear equations, which is iteratively iterated using Newton's method, and needs to provide the initial value and the function handle of the system of equations.

The fminsearch() function can solve the system of nonlinear equations by minimizing the objective function of Zheng Qiao, and the initial value and the function handle of the objective function need to be provided.

Kiss, process.

MATLAB can use the " function to solve solutions in linear equation assemblies.

1.Use the " function.

A system of linear equations of the form ax=b can be solved using the " " function, where a is the matrix of the first coefficients and b is a constant vector.

For example, a system of linear equations like this is required to be solved:

3x + 2y = 7

4x - 5y = 8

You can do this by following these steps:

``matlab

Define the coefficient matrix a and the constant vector b

a = 3, 2; 4, -5];

b = 7; -8];

Solve systems of linear equations.

x = a \ b;

Output solution. disp(x);

The result is as follows:

Explain that the number of solutions for the system of equations is x=2 and y=1.

Use the solve function. For example, solve a system of nonlinear equations x 2 + y 3 = 10

x^3-y^2=1

where x and y are the unknown quantities of the system of equations.

In the naming window of the MATLAB, type:

syms x y

x y]=solve('x^2+y=10','x^2-y^2=1','x','y')

That is, the output of the genus is calculated as:

x =(37^(1/2)/2 + 21/2)^(1/2)(21/2 - 37^(1/2)/2)^(1/2)-(21/2 - 1/2*37^(1/2))^1/2)-(1/2*37^(1/2) +21/2)^(1/2)y =- 37^(1/2)/2 - 1/237^(1/2)/2 - 1/2

You can learn how to use the solve function by entering help solve.

Let's participate in modeling!! We're doing it too.

Start by defining the function:

function f=fx(x)

f(1)=3*x(1)-cos(x(2)*x(3));

f(2)=x(1)^2-81*(x(2)+;

f(3)=exp(-x(1)*x(2))+20*x(3)+(10*pi-3)/3;

x=fsolve(@fx,[1,1,1]) and finally find x =

I'm glad to answer for you, first define the function myfun

function f = myfun(x)f = [3*x(1)-cos(x(2)*x(3));

x(1)^2-81*(x(2)+;

exp(-x(1)*x(2))+20*x(3)+(10*pi-3)/3];

The preceding function is defined in a file.

The main procedure is as follows:

x,fval]=fsolve(@myfun,[0,0,0]);

x(1)x(2)

x(3) is finally obtained.

x(1)=x(2)=

1.First, define the function myfun

function f = myfun(x)f = [3*x(1)-cos(x(2)*x(3));

x(1)^2-81*(x(2)+;

exp(-x(1)*x(2))+20*x(3)+(10*pi-3)/3];

2.The preceding function is defined in a file.

The main procedure is as follows:

x,fval]=fsolve(@myfun,[0,0,0]);

x(1)x(2)

x(3)3.Finally, we get:

x(1)=x(2)=

x(3)=Extended MaterialsIntroduction to MATLAB.

MATLAB is a commercial mathematics software produced by Mathworks in the United States, which is a high-level technical computing language and interactive environment for algorithm development, data visualization, data analysis and numerical calculation, mainly including MATLAB and Simulink.

Numerical solution of nonlinear equations.

Since the mid-60s of the 20th century, two new methods for solving nonlinear equations (1) have been developed. One is called the interval iteration method or interval Newton method, which uses interval variables instead of point variables for interval iteration, and each iteration step can determine the existence of uniqueness or no solution in the given interval solution.

You can use the solve function. Refer to the following below:

For example: x 2 + y 3 = 10

x^3-y^2=1

where x,y are the unknown quantities of the system of equations, enter :

y =- 37^(1/2)/2 - 1/2

syms x y

x y]=solve('x^2+y=10','x^2-y^2=1','x','y'The output evaluates to: x =

Use the solve function in the format solve(Equation 1, Equation 2,...Solve for variable 1, variable 2 ,...）

Among them, the equation "algebraic formula = 0" is only written as an algebraic formula, and if the variable is not written, it is automatically determined by findsym by default.

g=solve(eq1,eq2,…,val1,val2…The resulting g is an array of architectures that displays the result of each variable with instructions, e.g. syms x y

g=solve(x^2+y-8,x-y^2+y-10,x,y);