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- W2013302193 abstract "In this article we propose a procedure which generates the exact solution for the system A x = b , where A is an integral nonsingular matrix and b is an integral vector, by improving the initial floating-point approximation to the solution. This procedure, based on an easily programmed method proposed by Aberth [1], first computes the approximate floating-point solution x * by using an available linear equation solving algorithm. Then it extracts the exact solution x from x * if the error in the approximation x * is sufficiently small. An a posteriori upper bound for the error of x * is derived when Gaussian Elimination with partial pivoting is used. Also, a computable upper bound for |det( A )|, which is an alternative to using Hadamard's inequality, is obtained as a byproduct of the Gaussian Elimination process." @default.
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- W2013302193 date "1987-06-01" @default.
- W2013302193 modified "2023-09-29" @default.
- W2013302193 title "Error-free computer solution of certain systems of linear equations" @default.
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- W2013302193 doi "https://doi.org/10.1016/0377-0427(87)90002-1" @default.
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