[PDF] complexity of lu factorization

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  • What is the computational complexity of LU factorization?

    The most computationally intensive part of solving (1) is the LU factorization defined by (2).
    This operation has computational complexity of order O(n3) when A is a dense matrix, as compared to O(n2) for the solution phase.

  • Is LU decomposition faster?

    Solving linear equations
    In this case it is faster (and more convenient) to do an LU decomposition of the matrix A once and then solve the triangular matrices for the different b, rather than using Gaussian elimination each time.

  • Is LU factorization always possible?

    We have proved that not all square matrices have an LU factorization.
    However, we can always permute the rows of a matrix (i.e., repeatedly interchange them) so as to get an LU factorization, as illustrated by the following proposition.

  • Is LU factorization always possible?

    The LU factorization was a stable computation but not backward stable.
    Recall that an n×n permutation matrix P is a matrix with precisely one entry whose value is "1" in each column and row, and all of whose other entries are "0." The rows of P are a permutation of the rows of the identity matrix.

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