(Student Research Project) The Gauss-Huard algorithm is a variant of the Gauss-Jordan algorithm for solving dense linear systems. Both algorithms reduce the system to an equivalent diagonal system. However, the Gauss-Jordan method does more floating-point operations than Gaussian elimination, whereas the Gauss-Huard method does not. To preserve stability, the Gauss Huard method incorporates a pivoting strategy using column interchanges. An error analysis shows that the Gauss-Huard method is as stable as Gauss-Jordan elimination with an appropriate pivoting strategy. Read about these algorithms in papers by Dekker and Hoffmann [1989], Dekker, Hoffmann, and Potma [1997], Hoffmann [1989], and Huard [1979]. Carry out some numerical experiments by programming and testing the Gauss-Jordan and Gauss-Huard algorithms on some dense linear systems.
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