Syntax

x = linsolve(A,b [,method]);

Description

This function solves the equation

A*x = b;

Where A is a square matrix of arbitrary size n and x and b are vectors of size n.

Returns the inverse of square non-singular matrix A.

The last argument is a string that specifies the desired method to use.

The gmres method allows further steering of the method by specifying method parameters:

The lu, qr and gmres methods allow a non-square matrix A to be entered yielding a pseudoinverse.

Examples

A = [1,2;0,1+ramp(1)];

b = [1;5];

x = linsolve(A,b);

x2 = linsolve (A, b, 'qr');

x3 = linsolve (A, b, 'gmres tol=1e-8 ortho=4');

Limitations

A must be a non-singular square matrix.

Note

The following equations

A*x = b;

x = inverse(A)*b;

x = (A^-1)*b;

all lead in the calculation of the inverse of A and will give the same result as

x = linsolve(A,b);

For the inverse calculation, Cramers rule is used. This is a method which is fast for small matrix sizes. The linsolve function with the gmres method is superior to Cramers rule for larger matrix sizes.