A study of the effect of the choice of pivot elements on round-off errors in Gauss elimination Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/2227ms05m

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  • It is established folklore in numerical analysis, for solution of a square system of linear equations by Gauss elimination, that the standard method of choice of pivot elements is to search the entire suppressed matrix for the element largest in absolute value. However, it was felt by the author, that use of this method would not minimize round-off errors when operating with unstable matrices. By the use of FORTRAN programming on the equation Cx = b, where C is the inverse of the Hilbert matrix, for N = 5, 6, and 7, and b is a column matrix of N rows with each element equal 1, it is shown the use of the standard method of search does not minimize round-off errors incurred, and an alternative method is developed.
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