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### Other Factorizations

The QL and RQ factorizations are given by

and

These factorizations are computed by xGEQLF and xGERQF, respectively; they are less commonly used than either the QR or LQ factorizations described above, but have applications in, for example, the computation of generalized QR factorizations [2].

All the factorization routines discussed here (except xTZRQF and xTZRZF) allow arbitrary m and n, so that in some cases the matrices R or L are trapezoidal rather than triangular. A routine that performs pivoting is provided only for the QR factorization.

 Type of factorization Operation Single precision Double precision and matrix real complex real complex QR, general factorize with pivoting SGEQP3 CGEQP3 DGEQP3 ZGEQP3 factorize, no pivoting SGEQRF CGEQRF DGEQRF ZGEQRF generate Q SORGQR CUNGQR DORGQR ZUNGQR multiply matrix by Q SORMQR CUNMQR DORMQR ZUNMQR LQ, general factorize, no pivoting SGELQF CGELQF DGELQF ZGELQF generate Q SORGLQ CUNGLQ DORGLQ ZUNGLQ multiply matrix by Q SORMLQ CUNMLQ DORMLQ ZUNMLQ QL, general factorize, no pivoting SGEQLF CGEQLF DGEQLF ZGEQLF generate Q SORGQL CUNGQL DORGQL ZUNGQL multiply matrix by Q SORMQL CUNMQL DORMQL ZUNMQL RQ, general factorize, no pivoting SGERQF CGERQF DGERQF ZGERQF generate Q SORGRQ CUNGRQ DORGRQ ZUNGRQ multiply matrix by Q SORMRQ CUNMRQ DORMRQ ZUNMRQ RZ, trapezoidal factorize, no pivoting STZRZF CTZRZF DTZRZF ZTZRZF (blocked algorithm) multiply matrix by Q SORMRZ CUNMRZ DORMRZ ZUNMRZ

Next: Generalized Orthogonal Factorizations and Up: Orthogonal Factorizations and Linear Previous: Complete Orthogonal Factorization   Contents   Index
Susan Blackford
1999-10-01