Stability of Gauss-Huard Elimination for Solving Linear Systems

This paper considers elimination methods to solve dense linear systems, in particular a variant due to Huard of Gaussian elimination [13]. This variant reduces the system to an equivalent diagonal system just as GaussJordan elimination, but does not require more floating-point operations than Gaussian elimination. Huard's method may be advantageous for use in computers with hierarchical memory, such as cache, and in distributedmemory systems. An error analysis is given showing that Huard's elimination method is as stable as Gauss-Jordan elimination with appropriate pivoting strategy. This result was announced in [5] and is proven in a similar way as the proof of stability for Gauss-Jordan given in [4].