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computes the matrix inverse
x=inv(a)*b;Note that the SOLVE function is more accurate and efficient for this task.
A = {0 0 1 0 1, 1 0 0 1 0, 0 1 1 0 1, 1 0 0 0 1, 0 1 0 1 0}; b = {9,4,10,8,2}; /* find inverse and solve linear system */ Ainv = inv(A); x1 = Ainv*b; /* solve by using a more efficient algorithm */ x2 = solve(A,b);These statements produce the following output:
X1 X2 3 3 1 1 4 4 1 1 5 5
All matrix elements less than or equal to sing are now considered rounding errors of the largest matrix elements, so they are taken to be zero. For example, if a diagonal or triangular coefficient matrix has a diagonal value less than or equal to sing, the matrix is considered singular by the DET, INV, and SOLVE functions.
Previously, a much smaller singularity criterion was used, which caused algebraic operations to be performed on values that were essentially floating-point error. This occasionally yielded numerically unstable results. The new criterion is much more conservative, and it generates far fewer erroneous results. In some cases, you might need to scale the data to avoid singular matrices. If you think the new criterion is too strong, do the following:
If is an matrix, the INV function allocates an matrix in order to return the inverse. It also temporarily allocates an array in order to compute the inverse.
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