Figure Properties - SERC

inv
2-1214
while the statements
tic, z = A\b, toc
err = norm(z-x)
res = norm(A*z-b)
produce
elapsed_time =
0.6410
err =
7.1209e-006
res =
4.4509e-015
It takes almost two and one half times as long to compute the solution with
y = inv(A)*b as with z = A\b. Both produce computed solutions with about
the same error, 1.e-6, reflecting the condition number of the matrix. But the
size of the residuals, obtained by plugging the computed solution back into the
original equations, differs by several orders of magnitude. The direct solution
produces residuals on the order of the machine accuracy, even though the
system is badly conditioned.
The behavior of this example is typical. Using A\b instead of inv(A)*b is two
to three times as fast and produces residuals on the order of machine accuracy,
relative to the magnitude of the data.
Algorithm Inputs of Type Double
For inputs of type double, inv uses the following LAPACK routines to compute
the matrix inverse:
Matrix Routine
Real DLANGE, DGETRF, DGECON, DGETRI
Complex ZLANGE, ZGETRF, ZGECON, ZGETRI