Anasazi Version of the Day
Orthogonalization fault. More...
Stewart (SISC 2008) presents a Block Gram-Schmidt (BGS) algorithm with careful reorthogonalization. He defines an "orthogonalization fault" as happening when the second BGS pass does not succeed. This is possible in BGS, but not possible in (non-block) Gram-Schmidt, if you use Stewart's randomization procedure for the latter. Stewart gives an algorithm for recovering from an orthogonalization fault, but the algorithm is expensive: it involves careful reorthogonalization with non-block Gram-Schmidt. If the "throwOnReorthogFault" option is set, we choose instead to report the orthogonalization fault as an exception.