The partial pivoting
code SuperLU and the sequential option of the symmetric-pattern multifrontal code MA41 do not have fragmentation in their work arrays, and thus do not require garbage collection.
ALAN GEORGE AND ESMOND NG, Symbolic Factorization for Sparse Gaussian Elimination with Partial Pivoting, SIAM J.
ELEANOR CHU AND ALAN GEORGE, Gaussian Elimination with Partial Pivoting and Load Balancing on a Multiprocessor, Parallel Comput.
13 LU decomposition with partial pivoting DO 10 KK = KK,K+KS-1 DO 30 J =1,N TAU = A,(KK,J) 25 A(KK,J) = A(IMAX,J) 30 A(IMAX,J) = TAU DO 10 J = KK+KS,N DO 10 I = KK+1,N 10 A(I,J) = A(I,J) - A(I,KK) * A(KK,J)
Unless the compiler understands that row interchanges and column updates commute, LU decomposition with partial pivoting is not blockable.
In 1977, Bunch and Kaufman proposed a partial pivoting method, now known as the Bunch-Kaufman pivoting method, where a 1 x 1 or 2 x 2 pivot can be determined by searching at most two columns of the reduced matrix at each step .
HIGHAM, Stability of the diagonal pivoting method with partial pivoting, SIAM J.
PENA, Scaled pivots and scaled partial pivoting
strategies, SIAM J.