linsolve

Purpose

Solves \(Ax = b\) using the inverse function.

Format

x = linsolve(b, A)
Parameters:
  • b (NxK matrix) – data
  • A (NxN matrix) – data
Returns:

x (NxK matrix) – the linear solution of \(b/A\) for each column in b.

Examples

// Assign b
b = { 2, 3, 4 };

// Assign A
A = { 10 2 3, 6 14 2, 1 1 9 };

//  Solve Ax = b
x = linsolve(b, A);
print x
0.04586330
0.13399281
0.42446043

Remarks

linsolve() solves for x by computing \(inv(A) \times b\). If A is square and b contains more than 1 column, it is much faster to use linsolve() than the / operator. However, while faster, there is some sacrifice in accuracy.

A test shows linsolve() to be acccurate to within approximately 1.2e-11, while the slash operator / is accurate to within approximately 4e-13. However, the accuracy sacrifice can be much greater for poorly conditioned matrices.

See also

Functions qrsol(), qrtsol(), solpd(), cholsol()