Fast linear algebra is stable

In [12] we showed that a large class of fast recursive matrix multiplication algorithms is stable in a normwise sense, and that in fact if multiplication of n-by-n matrices can be done by any algorithm in O(n ) operations, then it can be done stably in O(n+ ) operations for any > 0. Here we extend this result to show that many standard linear algebra operations, including LU decomposition, QR decomposition, linear equation solving, matrix inversion, and determinant computation can also be done stably (in a normwise sense) in time O(n+ ).

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: James Demmel, Ioana Dumitriu, Olga Holtz
• Keywords: CORR 2006, Education, Linear Algebra Operations, Normwise Sense, Recursive Matrix Multiplication