Bareiss algorithm with fast multiplication (Determinant of Matrices with Integer Entries Determinant of Matrices with Integer Entries)

Time Complexity

$O(n^{4} L (\log(n)$ + L) \log(\log(n) + L))

Space Complexity

$O(n^{2}(n*log(n)$+nL)) bits

(Keeps track of $O(n^2)$ entries that have absolute value at most $O(n^{(n/2)}2^{(nL)})$)

Approximate?

Exact

Randomized?

No, deterministic

Model of Computation

Word RAM? (without O(1) multiplication)

Year

1968

Reference

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