QRUPDATE: A LIBRARY FOR FAST UPDATING OF QR AND CHOLESKY DECOMPOSITIONS ----------------------------------------------------------------------- The following operations are supported: QR rank-1 update (qr1up) Updates the QR factorization after an additive rank-1 update to the original matrix (A = A + u*v'). Works for full & economized factorization. QR column insert (qrinc) Updates the QR factorization after an inserting a column to the original matrix. Works for full & economized factorization. QR column delete (qrdec) Updates the QR factorization after an deleting a column from the original matrix. Works for full & economized factorization. QR column shift (qrshc) Updates the QR factorization after a circular shift of columns in the original matrix. Works for full & economized factorization. QR row insert (qrinr) Updates the QR factorization after an inserting a row to the original matrix. Works for full factorization only. QR row delete (qrder) Updates the QR factorization after an deleting a row from the original matrix. Works for full factorization only. Cholesky rank-1 update (ch1up) Updates the Cholesky factorization after positive rank-1 update A = A + u*u'. Cholesky rank-1 downdate (ch1dn) Updates the Cholesky factorization after positive rank-1 downdate A = A - u*u'. Cholesky symmetric insert (chinx) Updates the Cholesky factorization after a symmetric column/row insertion. Cholesky symmetric insert (chdex) Updates the Cholesky factorization after a symmetric column/row deletion. Cholesky symmetric shift (chshx) Updates the Cholesky factorization after a symmetric column/row left/right circular shift. LU rank-1 update (lu1up) Updates the LU factorization after a rank-1 update (A = A + u*v.'). No pivoting available. Faster than lup1up, but less stable. LU pivoted rank-1 update (lup1up) Updates a row-pivoted LUP factorization after a rank-1 update (A = A + u*v.'). Also updates the row permutation matrix. Slower than lu1up, but more stable. See the INSTALL file for installation details. Consult individual routines for documentation.