A quick way to check the complexity of an algorithm is to do an operation count. Count separately the number of multiplications and divisions needed for forward and back sub- stitution and (P)LU decomposition; to see that the computational expense of solving an n X n system Ax = b is O(n3). What about computing A-1?
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Then, we need to solve n linear systems of equations with the same (P)LU factors, each with a right-hand side vector of length n. Each of these systems can be solved using forward and back substitution, which takes O(n2) operations. Show more…
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