Tridiagonal matrix algorithm

Abstract: This paper considers elimination methods to solve dense linear systems, in particular a variant of Gaussian elimination due to Huard [13]. This variant reduces the system to an equivalent diagonal system just like Gauss-Jordan elimination, but does not require more floating-point operations than Gaussian elimination. To preserve stability, a pivoting strategy using column interchanges, proposed by Hoffmann [10], is incorporated in the original algorithm. An error analysis is given showing that Huard’s elimination method is as stable as Gauss-Jordan elimination with the appropriate pivoting strategy. This result is proven in a similar way as the proof of stability for Gauss-Jordan elimination given in [4]. Numerical experiments are reported which verify the theoretical error analysis of the Gauss-Huard algorithm.