Linear Algebra III
نویسندگان
چکیده
Complexity/Cost We stated last time that for a system of n equations in n unknowns (represented by an N × N matrix A), both LU and QR-factorization take time proportional to the cube of n (O(n3)). LU-factorization takes less time by a constant factor of around 2 as n gets large, this constant factor is dwarfed by the third power of the matrix dimension, however. Note that the theoretical “best-case” for the complexity of solving a linear system is O(n2), since there are n2 entries in the matrix A, and any correct algorithm would have to examine each entry.
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