WZ factorization via Abaffy-Broyden-Spedicato algorithms

Classes of‎ ‎Abaffy-Broyden-Spedicato (ABS) methods have been introduced for‎ ‎solving linear systems of equations‎. ‎The algorithms are powerful methods for developing matrix‎ ‎factorizations and many fundamental numerical linear algebra processes‎. ‎Here‎, ‎we show how to apply the ABS algorithms to devise algorithms to compute the WZ and ZW‎ ‎factorizations of a nonsingular matrix as well as the $W^TW$ and‎ ‎$Z^TZ$‎ ‎factorizations of a symmetric positives definite matrix‎. ‎We also describe the QZ and the‎ ‎QW factorizations‎, ‎with Q orthogonal‎, ‎and show how to appropriate the parameters of the ABS algorithms to compute these factorizations‎. ‎